Question $4$: $(10$ points$)$

Let $F(x,y,z)=(zarctan(y^2),z^{3}ln(x^2+1),x^{2}z).$ Find the flux $ofF$

across the surface $S,$ which $is$ part $of{x}^2+y^2+z=2$ that lies above

the plane $z=1$ and $is$ oriented upward.