The purpose of this paper is to study the validity of a Generalized Stokes' Theorem on integral currents for differential forms with singularities. We use techniques of non absolutely convergent integration in the spirit of W. F. Pfeffer, but our results are presented in the context of Lebesgue integration... We prove a Generalized Stokes' Theorem on integral currents of dimension $m$ in $\mathbb{R}^n$, whose singular sets have finite $m-1$ dimensional intrinsic Minkowski content. This condition applies to codimension $1$ mass minimizing integral currents with smooth boundary and to chains definable in an o-minimal structure. Conversely, we give examples of integral currents of dimension $2$ in $\mathbb{R}^3$ whose singular sets have finite or even null Hausdorff measure of dimension $1$ and which do not satisfy our version of Stokes' Theorem. (read more)