General Relativity/Stoke's theorem

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

$\int _{\mathcal {M}}d\omega =\int _{\partial {\mathcal {M}}}\omega$