Spin asymmetries of semi-inclusive cross sections for the production of positively and negatively charged hadrons have been measured in deep-inelastic scattering of polarized positrons on polarized hydrogen and He-3 targets, in the kinematic range 0.023 < x < 0.6 and 1 GeV2 < Q(2) < 10 GeV2. Polarized quark distributions are extracted as a function of x for up (u + (u) over bar) and down (d + (d) over bar) flavors. The up quark polarization is positive and the down quark polarization is negative in the measured range. The polarization of the sea is compatible with zero. The first moments of the polarized quark distributions are presented. The isospin non-singlet combination dq, is consistent with the prediction based on the Bjorken sum rule. The moments of the polarized quark distributions are compared to predictions based on SU(3)(f) flavor symmetry and to a prediction from lattice QCD. (C) 1999 Published by Elsevier Science B.V. All rights reserved