Hi, 1. The problem statement, all variables and given/known data I am now asked to prove that f: [0,1]->[0,1] defined thus f(0)=0 and f(x)=1/10n for every 1/2n+1<x<1/2n for natural n, is integrable. 2. Relevant equations 3. The attempt at a solution Would it suffice to show that f is continuous? I.e. that lim x->0 f(x) = f(0) = 0, since as x->0 n->infinity?