I recently started working through Arfken, Weber and Harris'Mathematical Methods for Physicists, when I came across the following integral:

$\displaystyle \int_{N_1}^{N_2} [x] f'(x) \, dx = \sum_{n=N_1}^{N_2-1} n \int_{n}^{n+1} f'(x)\, dx$

where $\displaystyle [x]$ is the integral part of $\displaystyle x$.

I don't understand how the RHS emerges from the LHS. Can someone please enlighten me as to what the hidden steps are? Thanks very much.

Andy