Compute E[X] if X has a probability density function given by

$\displaystyle f(x) = \begin{cases} c(1-x^2) & -1<x<1 \\ 0 & otherwise \end{cases}$

---------------------------------My work ---------------------------------

$\displaystyle E[X] = \int_{-1}^{1} x. f(x) dx = \int_{-1}^{1} x . [c (1-x^2)]dx = ......=0$.........Is this correct????