I'm working on this exercise from an old Spivak Differential Geometry book which I must be misunderstanding. The question reads:
Let $M$ and $N$ be compact $n$-dimensional manifolds with boundary and $M \subset N \setminus \partial N$. For any closed $(n-1)$-form $\omega$ on $N$ show $\int_{\partial M} \omega=\int_{\partial N} \omega$.
Both integrals seem to me to be trivially equal as by Stoke's theorem $\int_{\partial M} \omega=\int_M d\omega =\int_M 0=0$? Am I missing something here? Any external verification? I feel like I'm taking crazy pills, but this book has so many typos...