  In this paper we present the master integrals necessary for the analytic
calculation of the box diagrams with one electron loop (N_{F}=1) entering in
the 2-loop (\alpha^3) QED virtual corrections to the Bhabha scattering
amplitude of the electron. We consider on-shell electrons and positrons of
finite mass m, arbitrary squared c.m. energy s, and momentum transfer t; both
UV and soft IR divergences are regulated within the continuous D-dimensional
regularization scheme. After a brief overview of the method employed in the
calculation, we give the results, for s and t in the Euclidean region, in terms
of 1- and 2-dimensional harmonic polylogarithms, of maximum weight 3. The
corresponding results in the physical region can be recovered by analytical
continuation. For completeness, we also provide the analytic expression of the
1-loop scalar box diagram including the first order in (D-4).
