What is the area of the region between $y = x$ and $y = x^{2}$?

Explanation

1. 01

   They meet where $x^{2} = x$: $x = 0$ and $x = 1$, with the line above.

2. 02

   $\int_0^{1} (x - x^{2})\,dx = \frac{1}{2} - \frac{1}{3} = \frac{1}{6}$ square units.