In recent papers, Pichon and later on Sagar have dealt with the problem of computing the generalised Fermi-Dirac integrals. Both suggest Gauss-type quadratures differing only with respect to the form of the weight function used. This paper investigates the possibility of using the simple trapezoidal rule. By a suitable transformation of the variable of integration, it is possible to obtain high accuracies over the entire range of the physical parameters of interest.