$\int_{-\frac{1}{2}}^{\frac{1}{2}} f(x)dx$
$\int_{-\frac{1}{2}}^{\frac{1}{2}} x^{3}dx$
$\lim_{x->\frac{1}{2}}\left [ \frac{x^{4}}{4} \right ] - \lim_{x->-\frac{1}{2}}\left [ \frac{x^{4}}{4} \right ]$
= $\frac{1}{4}\left ( \frac{1}{16} - \frac{1}{16} \right )=0$