Integral involving an integral part

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

where is the integral part of .

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

Re: Integral involving an integral part

It looks pretty straight forward to me. One of the very first things you learn about integrals is that " ". I presume you will agree that . Extending that, the left side is equal to since that just breaks the integral into a sum of integrals. If x lies between n and n+ 1 then [x]= n so that .