The purpose of this article is an up-to-date, detailed, and rigorous presentation of the generalized least-squares procedure developed by our group to improve neutron cross-section evaluations, based on direct cross-section measurements by means of integral data. Both discrete and continuous (energy dependent) integral quantities are considered. Explicit expressions are derived for the best estimates of the cross sections in a continuous form, as well as in the multigroup approximation. The procedure is illustrated by results relating to the updated Los Alamos data on spherical metallic critical assemblies and the latest ENDF/B cross-section library. It is demonstrated that by minor modifications of the ENDF/B cross sections, most of the experimental data can be reproduced within their quoted uncertainties.