Evaluate $\displaystyle \int_{{C}}\vec{{{F}}}\cdot{d}\vec{{{r}}}$ where $\displaystyle \vec{{{F}}}={\left\langle-{3}{z},-{y},{4}{x}\right\rangle}$, and $\displaystyle {C}$ is given by $\displaystyle \vec{{{r}}}{\left({t}\right)}={\left\langle{t},{\sin{{\left({t}\right)}}},{\cos{{\left({t}\right)}}}\right\rangle},\ {0}\le{t}\le\pi$