Surface Integrals, Stokes & Divergence · Challenge problem

Let $E$ be the solid inside the cylinder $x^2 + y^2 = 4$, above the plane $z = 0$ and below the plane $z = x + 3$. Find the outward flux of $\mathbf F = (x^3 + yz,\ y^3 - xz,\ z)$ through the boundary of $E$. Give an exact answer in terms of $\pi$.