A numerical integration

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I have a discrete data file of $t$ and $f(t)$ of a unknown function. I have to do Laplace transformation to get $s$ and $f(s)$, $f(s)=\int f(t) e^{-st} dt$. So, I basically want to numerically integrate it. The $f(s)$ function will have some poles where the function diverges, I have to plot $f(s)$ versus $s$ to get the largest pole. I tried with Simpson's method. But largest pole has error in precision. What will be the correct numerical method for this particular problem?