Hi im kinda stuck on this question, any hints are appreciated

I got f:[1,infinity[ -> R, is a positive continious decresing function, and m < n for m,n belonging to N.

I need to show that ∫ from m+1 to n+1 f(x)dx <= sum from k=1 to n of f(k) - sum from k=1 to m of f(k) <= ∫ from m to n f(x)dx

Apologize for the setup, but hopefully its 'readable'