Surface integral where $S$ is the surface of a solid bounded by cylinder $x^2+z^2=4$ and planes $y=0$ and $y=3$.

Question

$$\iint_{S}\langle-3z^2,1-x,(y-2z)\rangle\,d\vec{s}$$ I am trying to solve this surface integral where $S$ is the surface of a solid bounded by cylinder $x^2+z^2=4$ and planes $y=0$ and $y=3$, I arrived with the Divergence theorem and cylindric coordinates in $$\int_{0 }^{2\pi}\int_{3 }^{0}\int_{-\sqrt{4-^2\cos^2\Theta} }^{\sqrt{4-^2\cos^2\Theta} }\,dz\,dr\,d\Theta, $$ but it doesn't have a solution, maybe mt limits are wrong?