  We present a general procedure for obtaining the coefficients of the scalar
bubble and triangle integral functions of one-loop amplitudes. Coefficients are
extracted by considering two-particle and triple unitarity cuts of the
corresponding bubble and triangle integral functions. After choosing a specific
parameterisation of the cut loop momentum we can uniquely identify the
coefficients of the desired integral functions simply by examining the
behaviour of the cut integrand as the unconstrained parameters of the cut loop
momentum approach infinity. In this way we can produce compact forms for scalar
integral coefficients. Applications of this method are presented for both QCD
and electroweak processes, including an alternative form for the recently
computed three-mass triangle coefficient in the six-photon amplitude
$A_6(1^-,2^+,3^-,4^+,5^-,6^+)$. The direct nature of this extraction procedure
allows for a very straightforward automation of the procedure.
