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:

Step 1 

Just integrate the function we have been doing – we get the answer .

Step 2 

Evaluate what this answer equals when we substitute the top number in (the 4):

                                                   

Step 3 

Evaluate what this answer equals when we substitute the bottom number in (1):

                                                    

Step 4 

Subtract step 3 from step 2:

                                                  

Note how the constant of integration cancels out.