Calculate $\displaystyle \int\int_{{S}}\overline{{{F}}}\cdot{d}\overline{{{S}}}$ where

$\displaystyle \overline{{{F}}}={\left\langle{3}{x}{y}^{{2}},{x}{e}^{{z}},{z}^{{3}}\right\rangle}$

$\displaystyle {S}$ is the surface of the solid bounded by the cylinder $\displaystyle {y}^{{2}}+{z}^{{2}}={9}$ and the planes $\displaystyle {x}=-{1}$ and $\displaystyle {x}={1}$