Evaluate each of the following integral: `int_(-1)^1x|x|dx`

Explanation

`\begin{aligned} I &=\int_{-1}^{1} x|x| d x \\ I &=-\int_{-1}^{0} x \cdot x+\int_{0}^{1} x^{2} \\ I &=-\int_{-1}^{0} x^{2}+\left[\frac{x^{3}}{3}\right]_{0}^{1} \\ I &=-\left[\frac{x^{3}}{3}\right]_{-1}^{0}+\frac{1}{3}(1-0) \\ I &=-\frac{1}{3}\left[(0-(-1)]+\frac{1}{3}\right.\\ I=&-\frac{1}{3} x \mid+\frac{1}{3}=-\frac{1}{3}+\frac{1}{3}=0 \\I=0\end{aligned}`