Let $\displaystyle F:R^+ \to R$ given by F(x) = x + floor(x), show that for $\displaystyle f: R^+ \to R$ that ($\displaystyle \mu_F$ Lebesgue-Stieltjes measure, that is $\displaystyle \mu_F(]a,b]) = F(b) - F(a)$)

$\displaystyle \int f d\mu_F = \int_0^\infty f(x) dx$ (= the normal Lebesgue integral) $\displaystyle + \sum_{n=1}^\infty f(n)$

Any help is appreciated. How do I start? Do I start by figuring out how the measure looks for general sets? I can 'see' the result if the function is constant on an interval, but the normal representation can be very different from this, example: 1 on the cantor set and 0 everywhere else. How do I make sure those cases are included?