I need a little help understanding how to compute a Lebesgue-Stieltjes integral. If $\{s_n\}_n$ is a sequence of real numbers such that $s_n>0$ $\forall n$ and the sum of all the $s_n$ isn't infinite, you can define a measure $\mu(B) = \sum_{n \in B}s_n$, where $B$ is a Borel set. This has a distribution function $F(x)=\sum_{n=1}^{[x]}s_n$.
So, lets say there is a Borel-Measurable function $f$, and I want to compute the Lebesgue Stieltjes integral $\int_{\mathbb{R}}fdF=\int_{\mathbb{R}}fd\mu$. How do I deal with the "$d\mu$" part here? Obvious i need to take the integral with respect to my measure but I am somewhat lost and confusing myself ever further.
Thanks!