Evaluate $\displaystyle \int_{{C}}\vec{{{F}}}\cdot{d}\vec{{{r}}}$ where $\displaystyle \vec{{{F}}}=<{y}^{{2}}{z},{x}{y}^{{2}},{x}{z}>$, and $\displaystyle {C}$ is given by $\displaystyle \vec{{{r}}}{\left({t}\right)}=<{t}^{{3}},{t},{5}>$, $\displaystyle \ {0}\le{t}\le{2}$