Use the divergence theorem to evaluate the surface integral \iint_{S} \underline{F} \cdot d \underline{S} \text { where the vector field is } \underline{F}=(3 x+1) \underline{i}+y\left(2 z^{2}+1\right) \underline{j}+\left(x^{3}+2 z y^{2}\right) \underline{k} and S is the cylindrical surface (without disks) specified by S=\left\{(x, y, z) \mid y^{2}+z^{2}=2,0 \leqslant x \leqslant 1\right\} oriented outwards.