= Solution
{c}
Let $V$ be a bounded region with piecewise smooth closed boundary $\partial V$, and let $\mathbf F$ be a <continuously differentiable vector field> on an open neighbourhood of its <closure>. The <divergence theorem> states
$$
\boxed{\iiint_V\nabla\cdot\mathbf F\,dV
=\iint_{\partial V}\mathbf F\cdot\mathbf n\,dS},
$$
where $\mathbf n$ is the outward <unit normal vector>. Thus the <volume integral> of the <divergence> equals the outward boundary <flux integral>. For a region containing a hole, the outward <unit normal vector> on its inner boundary points into that hole.
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