Average Value Function and Equivalent Periodic Function

This is a homework problem and I'm not even sure where to start with it. The problem reads: "Show that if f(x) has period p, the average value of f is the same over any interval of length p. Hint: $\displaystyle \int_a^{a+p}f(x) dx $ as the sum of two integrals (a to p, and p to a+p) and make the change of variable x = t+p in the second integral."

Okay so I know how to write the hint out and I get the point that f(t+p) = f(t) but what am I actually supposed to write out? I don't know out to transform this integral. Where do I start after writing out the 'hint'?