I have the integral
$$\int_0^1\lfloor nx\rfloor\mathrm dx=\sum_{k=0}^{n-1}k\frac1n=\frac{n-1}2$$
where $n\in\Bbb N_{\ge 1}$ and $\lfloor{\cdot}\rfloor$ is the floor function. But when I try to evaluate in Mathematica with this code:
Refine[Integrate[Floor[n*x], {x, 0, 1}], n ∈ Integers && n > 0]
It stays unevaluated. How I can evaluate it?