General Relativity/Stoke's theorem

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

$\underset{ℳ}{\int }d\omega =\underset{\partial ℳ}{\int }\omega$