  Recently, we evaluated the virtual cross-section for Bhabha scattering in
pure QED, up to corrections of order alpha^4 (N_F =1). This calculation is
valid for arbitrary values of the squared center of mass energy s and momentum
transfer t; the electron and positron mass m was considered a finite, non
vanishing quantity. In the present work, we supplement the previous calculation
by considering the contribution of the soft photon emission diagrams to the
differential cross-section, up to and including terms of order alpha^4 (N_F=1).
Adding the contribution of the real corrections to the renormalized virtual
ones, we obtain an UV and IR finite differential cross-section; we evaluate
this quantity numerically for a significant set of values of the squared center
of mass energy s.
