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

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

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

where $C$ is anticlockwise when viewed from large $z,$ and

$F_{?}=(x^3+3y)i_{+}(siny-2z)j_{+}(-3x^{2}y+cosz)k_{?}$

$I=$