We examine the redistribution of the in-plane optical spectral weight in the normal and superconducting state in trilayer Bi2Sr2Ca2Cu3O10 (Bi2223) near optimal doping (Tc=110K) on a single crystal via infrared reflectivity and spectroscopic ellipsometry. We report the temperature dependence of the low-frequency integrated spectral weight W(Ωc) for different values of the cutoff energy Ωc. Two different model-independent analyses consistently show that for Ωc=1eV, which is below the charge transfer gap, W(Ωc) increases below Tc, implying the lowering of the kinetic energy of the holes. This is opposite to the BCS scenario, but it follows the same trend observed in the bilayer compound Bi2Sr2CaCu2O8 (Bi2212). The size of this effect is larger in Bi2223 than in Bi2212, approximately scaling with the critical temperature. In the normal state, the temperature dependence of W(Ωc) is close to T2 up to 300K.