Consider a Riemannian manifold with bounded Ricci curvature |Ric|\leq n-1 and the noncollapsing lower volume bound Vol(B_1(p))>v>0. The first main result of this paper is to prove the previously conjectured L^2 curvature bound \fint_{B_1}|\Rm|^2 < C(n,v). In order to prove this, we will need to first show the following structural result for limits. Namely, if (M^n_j,d_j,p_j) -> (X,d,p) is a GH-limit of noncollapsed manifolds with bounded Ricci curvature, then the singular set S(X) is n-4 rectifiable with the uniform Hausdorff measure estimates H^{n-4}(S(X)\cap B_1)