  The method for functional reduction of Feynman integrals, proposed by the
author, is used to calculate one-loop integrals corresponding to diagrams with
four external lines. The integrals that emerge from amplitudes for the
scattering of light by light, the photon splitting in an external field and
Delbr\"{u}ck scattering are considered. For master integrals in $d$ -
dimensions, new analytic results
  are presented. For $d=4$, these integrals are given by compact expressions in
terms of logarithms and dilogarithms.
