  Recasting the $N$-point one loop scalar integral from Feynman to Schwinger
parameters gives an integrand with a Gaussian form. By application of a Fourier
transform, it is easy to derive explicit expressions for the two, three and
four-point functions. The Fourier transformation disentangles singularities in
the complex plane and extract their contribution as two-point functions in two
dimensions. We explicitly derive a one dimensional expression for the (4D)
four-point function whose integrand involves only square root and arcsine
functions. This report is a condensed version of the approach developed in
\cite{Benhaddou2016} which does not make use of probabilistic jargon.
