You have a series of point samples of a continuous signal. You can approximate the original signal using that data as a series of rectangles, more accurately as a series of trapezoids, and usually even more accurately as a series of quadratic functions. There are various other techniques for obtaining accurate numeric approximations of the integral, how well they perform depends on the signal and hardware available.

Enthalpy: the signal should be properly filtered beforehand, yes. There should not be any frequency components higher than half the sampling frequency, or you get aliasing artifacts (though you can actually use this to your advantage, undersampling a signal to demodulate a low frequency signal from a high frequency carrier...but this is another subject entirely). This *is* integration (with a damping factor, so only high frequency signals integrate to near 0 over a full period), but not the application of it that I was talking about. Integrating acceleration to obtain velocity with analog electronics is not going to be doable over a long enough time period to output any kind of accurate velocity reading without some rather tricky design to minimize leakages that would cause the integrator to drift slowly without any acceleration. And forget about taking changes in vehicle orientation into account with gyroscope sensors.

Agreed on the sonar. You could get a not-very-useful airspeed sensor, but results from a sonar ground speed sensor would be terribly dependent on the type of ground, variations in shape, motion of the vehicle on its suspension, and sonar requires signal processing that is significantly more difficult to do than handling the output of an accelerometer, and depending on how far you go with designing your own, it gets into driver and amplifier design.