So far, we have studied derivatives, which is a method for extracting information about the rate of change of a function. But as you may have realized, integration is the reverse of the earlier problems.
In integration, we find the area underneath a curve. For example, if we have a car and our function gives us its velocity, the area under the curve will give us the distance it has traveled between two points.
Let's suppose we have the curve 
, and the area under the curve between x = a (the lower limit) and x = b (the upper limit, also written as [a, b]) is S. Then, we have the following:
The diagramatical representation of the ...
