Let $\frac{x^2}{2^2}+\frac{y^2}{3^2}=1$ be a surface $$ in $(x,y,z)-$space.

Let $C$ be the curve formed by the intersection of the plane $z=y-3x+1$ with $.$

Evaluate $I=o{\displaystyle \underset{C}{\overset{\phantom{}}{}}}{F}_{*}d{r}_{?},$

where $C$ is anticlockwise when viewed from large $z,$ and $F_{?}=(x^3-2y)i_{+}(siny-3z)j_{+}(-2x^{2}y+cosz)k_{?}I=$