Answer
$\frac{1}{6}$
Work Step by Step
Set up the integration to find the area under the curve on the interval [0,1] (given by pink region)
$\int_0^1 (x-x^2) dx$
$[\frac{1}{2}x^2 - \frac{1}{3}x^3]_0^1$, Evaluate the definite integral
$(\frac{1}{2} - \frac{1}{3}) - (0)$, Simplify
$\frac{1}{6}$
