Is it true that the surface integral over any closed surface (we are in $\mathbb R^3$) of the normal vector $\hat n$ of that surface, say $\hat n$ is pointing outward, is zero? In other words, is it true that
$$\iint_S \hat n \ dS = 0$$
for any closed surface $S$?
I recently ran across such an integral and while intuitively it would seem to have to be zero (it's quite obvious if the closed surface is a cube or a sphere), is it true for any closed surface and what would be the best way of proving this statement?