Let $\displaystyle \vec F(x,y,z)=(P(x,y,z),Q(x,y,z),R(x,y,z))$ be a vector field on $\displaystyle \mathbb R^3$ with continuous partial derivatives, and $\displaystyle S$ a smooth orientable surface. Show that

$\displaystyle \iint_S \vec F \cdot \vec{dS} = \iint_S Pdydz + Qdzdx+Rdxdy$.