The equations governing the perturbations of the Schwarzschild metric satisfy the Regge-Wheeler-Zerilli-Moncrief system. Applying the technique introduced in [2], we prove an integrated local energy decay estimate for both the Regge-Wheeler and Zerilli equations. In these proofs, we use some constants that are computed numerically. Furthermore, we make use of the r^p hierarchy estimates [13, 32] to prove that both the Regge-Wheeler and Zerilli variables decay as t^-3/2 in fixed regions of r.