In La2-xSrxCuO4 (LSCO) the spectral weight W=integralOmega0sigma(ab)1(omega,T)domega [where sigma(ab)1(omega,T) is the ab-plane conductivity] obeys the same law W=W0-BOmegaT2 as in a conventional metal such as gold, for any Omega up to the plasma edge. However, in LSCO BOmega points toward correlation effects and, unlike in gold, is related to an energy scale tT<<t0 approximately W0. The Ferrell-Glover-Tinkham sum rule is fulfilled in LSCO superconductors for Omega greater than or approximately equal to 2000 cm(-1).