Let $F$ be a continuous vector field; then: $$\iint_{S}F d\vec s=F(Q)n(Q)A(S)$$ for some $Q \in S$ and $A(S)$ is the area of $S$.
Firstly, I arrived at $\iint_{D}fg dA=f(Q) \iint_{D}g$ dA if $g \geq 0$ and $f$ continuous.
But now,$$\iint_{S}F d\vec s=\iint_{S}Pdx+Qdy+Rdz$$ but I can't see how to use the first result for arriving at $F(Q)$. Any suggestions?