Question 287433
First, find where x=x^2 (this gives the end points of the closed interior). This occurs when 1=x and 0=x. So, we are interested in the closed interval [0,1].

Now, you will note by graphing that x>=x^2 throughout [0,1]. IE. .5>.25 etc.

So we integrate from 0 to 1 of (x-x^2)dx.

This is (x^2/2)  -(x^3/3) evaluated from 0 to 1 so we have (1/2)-(1/3)=1/6.