Answer
$\dfrac{1}{4}$
Work Step by Step
From the graph we can see that the area bounded by the graphs of the equations goes from $x=0$ to $x=1$
$\displaystyle \int_{0}^{1} [x-x^3]dx = \bigg[ \dfrac{x^2}{2} - \dfrac{x^4}{4}\bigg] \Bigg \rvert_{0}^{1} = \dfrac{1^2}{2}-\dfrac{1^4}{4} - \bigg[ \dfrac{0^2}{2}-\dfrac{0^4}{4}\bigg] = \dfrac{1}{2}-\dfrac{1}{4} - \bigg[ 0\bigg] = \dfrac{1}{2}-\dfrac{1}{4} = \dfrac{1}{4}$
