Integration on k-1 form

Question

If $\omega$ is a $k-1$ form on a closed $k$-dimensional manifold $M$ then $\int_M d \omega = 0$.

I'm looking for a short proof to this problem, would Stokes be helpful?

Answer 1

Yes $$\int_M d\omega =\int_{\partial M} \omega=0$$ since $\partial M=\emptyset$ beause $M$ is closed.