Let $\mathbf{F}(x,y,z)=z\tan(y^2)\mathbf{i} + z^3\ln(x^2+1)\mathbf{j} - 3\mathbf{k}$. Use the Divergence Theorem to find the flux of $\mathbf{F}$ across the part of the paraboloid $x^2+y^2+z=2$ that lies above the plane $z=1$ and is oriented upwards.

$\int\int_S \mathbf{F} \cdot \ d \mathbf{S}=$