  We calculate the two-loop virtual, UV renormalized corrections at order
\alpha^4 (N_F=1) in QED to the Bhabha scattering differential cross section,
for arbitrary values of the squared c.m. energy s and momentum transfer t, and
on-shell electrons and positrons of finite mass m. The calculation is carried
out within the dimensional regularization scheme; the remaining IR divergences
appear as polar singularities in (D-4). The result is presented in terms of 1-
and 2-dimensional harmonic polylogarithms, of maximum weight 3.
