Double-polarization asymmetries for inclusive ep scattering were measured at Jefferson Lab using 2.6 and 4.3 GeV longitudinally polarized electrons incident on a longitudinally polarized NH3 target in the CLAS detector. The polarized structure function g(1)(x,Q2) was extracted throughout the nucleon resonance region and into the deep inelastic regime, for Q(2)=0.15-1.64 GeV2. The contributions to the first moment Gamma(1)(Q2)= integral g(1)(x,Q2) dx were determined up to Q(2)=1.2 GeV2. Using a parametrization for g(1) in the unmeasured low x regions, the complete first moment was estimated over this Q2 region. A rapid change in Gamma(1) is observed for Q2<1 GeV2, with a sign change near Q(2)=0.3 GeV2, indicating dominant contributions from the resonance region. At Q(2)=1.2 GeV2 our data are below the perturbative QCD evolved scaling value.