Calculus  Integration  Main Page.
As noted on the Calculus historical development page:
Leibniz began his development of Calculus from the study of areas and volumes.
Newton began his development of Calculus with the study of the continuous movement of a point
which led him to examine gradients of curves.
As they extended their work individually, both men saw the significant overlap in their theoretical work.
So integration was the field and the technique which was the first focus of development by Leibniz.
It is handy to remember these links:
Integration is used to calculate area and volume.
Differentiation is used to calculate gradients and slopes of curves.
Antidifferentiation.
The term antidifferentiation is synonymous with indefinite integration or primitive integration.
The technique of antidifferentiation is
used when we want to find the function whose derivative is what we are now given.
Hence an antiderivative is sometimes referred to as a primitive function or as an indefinite integral.
So if we have a function F(x), its derivative might be called f(x). So F '(x) = f(x).
Don't get too concerned about the distinction. Just think:
If we have F(x), its derivative is F '(x) which we can call f(x).
When we go backwards, then f(x) integrates to become the antiderivative F(x).
If we substitute values for the original function F(x) into the antiderivative, we can create the location constant.
From this page of the site, integration resources related to basic functions can be accessed. For trigonometric, exponential and logarithmic functions, access the separate main pages from the main menu.
The resources which can be accessed directly are: 
1. Approximation methods for finding areas or integrals. 
2. Basic integration approaches. 
3. Reverse Chain Rule questions. 
4. Differentiate ... hence find questions. 
5. Other integration by substitution. 
6. Applications questions. 
Learning area.  Resource. 
1. Approximation methods for finding areas and evaluating integrals.  
Area of a basic trapezium.  See Trapezoidal Rule  Main Page. 
Trapezoidal Rule (noncalculus courses). 
See Trapezoidal Rule  Main Page. 
Trapezoidal Rule (Calculus courses). 

Review of finding the area of a trapezium.  
Review of the steps for applying the trapezoidal rule to find area or volume.  
Trapezoidal Rule  Test Yourself 1.  
Trapezoidal Rule  Test Yourself 1  Solutions. 

2. Basic strategies for integration (antidifferentiation).  
Steps to follow for basic integration.  
Basic integration  Test Yourself 1.  
Basic integration  Test Yourself 1  Solutions. 

Basic integration  Test Yourself 2.  
Basic integration  Test yourself 2  Solutions. 

3. Integration by substitution  Reverse Chain Rule . 

Basic functions  Concept of the technique and steps to follow when using the Reverse Chain Rule. 
Reverse Chain Rule  Test Yourself 1.  
Reverse Chain Rule  Test Yourself 1  Solutions. 

Exponential functions  Reverse Chain Rule  Exponentials  Test Yourself 1. 
Reverse Chain Rule  Exponentials  Test Yourself 1  Solutions. 

Logarithmic functions  Reverse Chain Rule  Logarithms  Test Yourself 1. 
Reverse Chain Rule  Logarithms  Test Yourself 1  Solutions. 

Trigonometric functions.  Reverse Chain Rule  Trig functions  Test Yourself 1. 
Reverse Chain Rule  Trig functions  Test Yourself 1  Solutions. 

Multifunction.  Reverse Chain Rule  Multifunction  Test Yourself 1. 
Reverse Chain Rule  Multifunction  Test Yourself 1  Solutions. 

4. Differentiate ... hence find.  
Concept of the technique and the steps to follow for these types of questions.  
Basic functions.  Differentiate ... hence find  Test Yourself 1. 
Differentiate ... hence find  Test Yourself 1  Solutions.  
Exponential functions.  Differentiate (exp. function) ... hence find  Test Yourself 1. 
Differentiate (exp. function) ... hence find  Test Yourself 1  Solutions. 

Logarithmic functions.  Differentiate (log function) ... hence find  Test Yourself 1. 
Differentiate (log function) ... hence find  Test Yourself 1  Solutions 

Trigonometric functions.  Differentiate (trig function) ... hence find  Test Yourself 1. 
Differentiate (trig function) ... hence find  Test Yourself 1  Solutions 

Mixed functions.  Differentiate (mixed functions) ... hence find  Test Yourself 1. 
Differentiate (mixed functions) ... hence find  Test Yourself 1  Solutions. 

5. Other Integration by substitution  extension.  Extended substitution  Test Yourself 1. 
Extended substitution  Test Yourself 1  Solutions.  
6. Applications including calculating areas with calculus.  
Steps to apply for finding areas under curves or between two curves.  
Integration  Areas  Test Yourself 1.  
Integration  Areas  Test Yourself 1  solutions.  
Integration  Areas  Test Yourself 2.  
Integration  Areas  Test Yourself 2  solutions. 