Let $M$ be a manifold and $S$ a smooth imbedded hypersurface $S \subset M$ that divides $M$ into two disjoint connected components: $M \setminus S \simeq M^1 \cup M^2$.
Is Stokes theorem, stated as
$\int_M d\omega =\int_{\partial M} \omega$ ,
still valid if $\omega$ takes an infinite value at $S$? We assume that $S$ does not intersect with the boundary of $M$, i.e. $S \cap \partial M = \oslash$?