  The purpose of this paper is to study the validity of Stokes' Theorem for
singular submanifolds and differential forms with singularities in Euclidean
space. The results are presented in the context of Lebesgue Integration, but
their proofs involve techniques from gauge integration in the spirit of
R.~Henstock, J.~Kurzweil and W.~F.~Pfeffer. We manage to prove a generalized
Stokes' Theorem on integral currents of dimension $m$ whose singular sets have
finite $m-1$ dimensional intrinsic Minkowski content. This condition applies in
particular to codimension $1$ mass minimizing integral currents with smooth
boundary and to semi-algebraic chains. Conversely, we give an example of
integral current of dimension $2$ in $\mathbb{R}^3$, with only one singular
point, to which our version of Stokes' Theorem does not apply.
