The spin structure functions g, for the proton and the deuteron have been measured over a wide kinematic range in x and Q(2) using 1.6 and 5.7 GeV longitudinally polarized electrons incident upon polarized NH3 and ND3 targets at Jefferson Lab. Scattered electrons were detected in the CEBAF Large Acceptance Spectrometer, for 0.05 < Q(2) < 5 GeV2 and W < 3 GeV. The first moments of g(1) for the proton and deuteron are presented - both have a negative slope at low Q(2), as predicted by the extended Gerasimov-Drell-Hearn sum rule. The first extraction of the generalized forward spin polarizability of the proton gamma(p)(0) is also reported. This quantity shows strong Q(2) dependence at low Q(2). Our analysis of the Q(2) evolution of the first moment of g, shows agreement in leading order with Heavy Baryon Chiral Perturbation Theory. However, a significant discrepancy is observed between the gamma(p)(0) data and Chiral Perturbation calculations for gamma(p)(0), even at the lowest Q(2). (C) 2009 Elsevier B.V. All rights reserved.