The aim of the paper is to provide, by an approach based on the Monch fixed point theorem, existence results for the semilinear evolution problem with distributed measures 1 $$ \textstyle\begin{cases} dx=(-Ax+f(t,x))\,dt+dg, \quad t\in[0,1], x(0)=x_{0}, \end{cases} $$ where −A is the infinitesimal generator of a (uniformly or strongly) continuous semigroup $\{T(t),t\geq0\}$ of bounded linear operators, f is not necessarily continuous and $g:[0,1]\to X$ is a regulated function. Working with Kurzweil-Stieltjes integrals and using a measure of non-compactness allows us to relax the assumptions on the semigroup, on f and g comparing to some already known results.