The integral \(S=\int^{b}_{a}\phi (x)e^{\nu h(x)}dx\) is transformed via \(z=h(x)\) into \(S=\int_{C}\phi (x(z))\frac{e^{\nu z}}{h'(x(z))}dz\) in order to evaluate S numerically. The choice of \(x_ k\) on the interval [a,b] for using two different quadrature formulas is discussed. The performance of the proposed approach is demonstrated with the example \(S=\int^{b}_{a}e^{\nu ix^ 2}dx,\) with \(a=1\), \(b=2\) and \(a=0\), \(b=1\), for various values of \(\nu\in [20,10000]\). i is the imaginary unit \(\sqrt{-1}\).