Answer
$$A = \frac{1}{2} $$
Work Step by Step
From the graph, we can see that $x \geq x^{3}$ on the interval $[0,1]$; therefore, the area between the two curves is $$A=2\displaystyle\int_{0}^{1} x-x^{3} \space dx$$ $$A = 2 \bigg[\frac{x^{2}}{2} - \frac{x^{4}}{4} \bigg]^{1}_0$$ $$A=2\bigg[\frac{1}{2}-\frac{1}{4}\bigg]=\frac{1}{2}$$
