General Relativity/Stoke's theorem

Stokes' Theorem states that if there is an n-dimensional manifold $\mathcal{M}$ with boundary $\partial\mathcal{M}$, and if there is a form ω defined on the manifold, then the following is true:

$\int_{\mathcal{M}}d\omega = \int_{\partial\mathcal{M}}\omega$