Let $M$ be an oriented $r$ dimensional differentiable manifold with a piecewise differentiable boundary $\partial M$ Further, let $\partial M$ have the orientation induced by $M$ If $\omega$ is an $(r-1)$ form on $M$ with compact support, whose components have continuous first partial derivatives in any coordinate chart, then $$ \int_M \dd \omega = \int_{\partial M} \omega.$$