  We present methods for evaluating the Feynman parameter integrals associated
with the pentagon diagram in 4-2 epsilon dimensions, along with explicit
results for the integrals with all masses vanishing or with one non-vanishing
external mass. The scalar pentagon integral can be expressed as a linear
combination of box integrals, up to O(epsilon) corrections, a result which is
the dimensionally-regulated version of a D=4 result of Melrose, and of van
Neerven and Vermaseren. We obtain and solve differential equations for various
dimensionally-regulated box integrals with massless internal lines, which
appear in one-loop n-point calculations in QCD. We give a procedure for
constructing the tensor pentagon integrals needed in gauge theory, again
through O(epsilon^0).
