Find the area bounded by the curves `y=xa n dy=x^3dot`

Explanation

The curve intersect at `{x}=-1, {y}=-1 ; {x}=0, {y}=0` and `{x}=1, {y}=1` Therefore area `=-int_{-1}^{0}(x^{3}-x) d x+int_{0}^{1}(x-x^{3}) d x`


`=-[frac{x^{4}}{4}-frac{x^{2}}{2}]_{-1}^{0}+[frac{x^{2}}{2}-frac{x^{4}}{4}]_{0}^{1}`


`=-(frac{1}{4}-frac{1}{2})+(frac{1}{2}-frac{1}{4})=-frac{1}{2}+1=frac{1}{2}`