Question: Determine whether the given function is a probability density function

\[f\left( x \right)=\left\{ \begin{aligned} & \frac{\text{3}}{\text{2}}{{x}^{\text{2}}}+2x\text{ for }-1\le x\le 1 \\ & 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{otherwise} \\ \end{aligned} \right.\]