criteria for integrability (analysis)

Define f(x) = x^2 for all x in [0,1]. For each natural number n, compute L(f,Pn) and U(f,Pn), where Pn is the regular partition of [0,1] into n subintervals.Then use the Integrability Criterion to show that the function f:[0,1]->R is integrable.

I've already figured out that I can use the sum as k=1,2,3,....n for k^2 = n(n+1)(2n+1)/6 in the question somehow.