Let $\omega_1,\omega_2$ be two n-forms on a $n$-dimensional manifold $M$.

Now, imagine we have for every open $N \subset M$ that

$$\int_{N}\omega_1 = \int_N \omega_2.$$

Can anybody show me how to prove that both forms are equal?- I suspect that this is true as it sounds natural, although I don't know for sure.