As I mentioned in my comment, the easiest way to integrate a list of values is to use `Interpolation` with `Integrate` or `NIntegrate`. As [Jens noted](https://mathematica.stackexchange.com/questions/26882/simpsons-rule-with-listconvolve-or-listcorrelate#comment83803_26882), the upgrade information for `ListIntegrate`, an obsolete function also mentions the same thing. For the sake of completeness, here's how you'd do it: With[{if = Interpolation[(* list of {x, y} pairs *), InterpolationOrder -> k}, Integrate[if[x], {x, Sequence @@ if["Domain"][[1]]}] ] If you really do wish to use Simpson's rule specifically (perhaps, for a homework or to reproduce some other result), you can also do what Daniel suggested, which is to set up the vector for Simpson's rule (or the 3/8ths rule), $\{1,4,2,4,2,\ldots,4,2,1\}$ and use `Dot`.