  We show how Stokes' Theorem, in the fashion of the Generalised Cauchy
Formula, can be applied for computing double-cut integrals of one-loop
amplitudes analytically. It implies the evaluation of phase-space integrals of
rational functions in two complex-conjugated variables, which are simply
computed by an indefinite integration in a single variable, followed by
Cauchy's Residue integration in the conjugated one. The method is suitable for
the cut-construction of the coefficients of 2-point functions entering the
decomposition of one-loop amplitudes in terms of scalar master integrals.
