  The method for obtaining functional equations, recently proposed by one of
the authors, is applied to one-loop box integrals needed in calculations of
radiative corrections to heavy-quark production and Bhabha scattering. We
present relationships between these integrals with different arguments and box
integrals with all propagators being massless. It turns out that functional
equations are rather useful for finding imaginary parts and performing analytic
continuations of Feynman integrals. For the box master integral needed in
Bhabha scattering, a new representation in terms of hypergeometric functions
admitting one-fold integral representation is derived. The hypergeometric
representation of a master integral for heavy-quark production follows from the
functional equation.
