Boys' Function F_m(z) that appears in the quantum mechanics of Gaussian Type Orbitals is a special case of Kummer's confluent hypergeometric function. We evaluate its integral representation of a product of a power and an exponential function over the unit interval with the numerical Gauss-Jacobi quadrature. We provide a C function boysGaussJacobi(int m, double z) for real positive valuesof the argument z which basically employs a table of the weights and abscissae of the quadrature rule for integer quantum numbers m<= 129 copied from https://vixra.org/abs/1709.0304 We provide a C function boysGaussJacobiC(int m, complex double z) for complex values which uses a lookup table on a grid of reference values of z as detailed in https://doi.org/10.1023/B:NUMA.0000040063.91709.58 . [https://zenodo.org/records/3603249]