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

A simple expression for the four-point scalar function from Gaussian integrals and Fourier transform