Stationary phase method for two stationary points

Question

I have a function $\psi(t)$ which has two stationary points at $t=a$ and $t=b$ and I want to find the asymptotic form of the integral $I(x)=\int_{a}^{b}f(t)e^{ix\psi(t)}dt$. Bender&Orzsag talks about the approximation around a single stationary point, namely the lower limit of the integral, but I'm not sure how to extend it to the case when both the limits are stationary points. Any help would be appreciated. TIA!