Surface Integrals, Stokes & Divergence · Medium problem

The helicoid $S$ is parametrized by $\mathbf r(u, v) = (u\cos v,\ u\sin v,\ v)$ for $0 \le u \le 1$, $0 \le v \le 2\pi$, oriented by the normal $\mathbf r_u \times \mathbf r_v$. Find the flux of $\mathbf F = (x, y, z)$ through $S$. Give an exact answer.