  This article is the first of a series of three presenting an alternative
method to compute the one-loop scalar integrals. This novel method enjoys a
couple of interesting features as compared with the method closely following 't
Hooft and Veltman adopted previously. It directly proceeds in terms of the
quantities driving algebraic reduction methods. It applies to the three-point
functions and, in a similar way, to the four-point functions. It also extends
to complex masses without much complication. Lastly, it extends to kinematics
more general than the one of physical e.g.\ collider processes relevant at one
loop. This last feature may be useful when considering the application of this
method beyond one loop using generalised one-loop integrals as building blocks.
