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:

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