1. The problem statement, all variables and given/known data Does pointwise convergence imply convergence of integral on C[0,1]? 2. Relevant equations 3. The attempt at a solution Would like to verify that f(t)=t^n is a counter example of this. Pointwise convergence goes to 0 on [0,1) and 1 on . Norm(1) is unbounded. I hope that right. It looks so small written out, but took almost 2 hours putting it together. Thanks in advance.