The mathematical expression above is called an indefinite integral. There is also a definite integral. The definite integral is like an indefinite integral except two numbers are specified between which to integrate. An example of a definite integral is:
The two numbers specified are 1 and 4. To evaluate what this definite integral is equal to, you do the following:
Just integrate the function we have been doing – we get the answer .
Evaluate what this answer equals when we substitute the top number in (the 4):
Evaluate what this answer equals when we substitute the bottom number in (1):
Subtract step 3 from step 2:
Note how the constant of integration cancels out.