If I have a vector of data that is equally spaced in time. What is the best numerical method for integrating this data?
The best method is determined by the nature of the data, ie. the quantity, quality, and general behavior (linear, quadratic, exponential), etc.
Do some searches on the Finite Volume method and integration approaches. Lots of work is done in CFD/CSD coming up with stable, conservative approaches. It might be a little bit overkill than say, the trapezoid rule, but if you're looking for high-accuracy, that'd be the way to go.