vec$(F)(x,y,z)=($:$x^2,y^2,z^2$:$),S$ is a surface bounded by the cylinder $x^2+y^2=1,z=-1$ and $z=1.$

Evaluate the outward flux ${\displaystyle \underset{S}{\overset{\phantom{}}{}}}$vec$(F)*vec(N)dS$ using the Divergence Theorem.