numeric integration of datapoints

I have time (dt) acceleration (Acc) data points. I need to plot velocity (vel) and displacement (disp) vs time and also calculate peak velocity (V_max) and peak displacement (d_max). I have used "cumtrapz" to do so as below:

vel=cumtrapz (dt,Acc); % velocity

disp=cumtrapz(dt,vel); % displacement

v_max=max(vel);

d_max=max(disp);

However, the peak velocity and displacement are not accurate. Is there a way to approximate them more accurately?

[Walter Roberson]

How do you know that your calculated values are not accurate?

[Mos_bad]

Because the data are ground motions and downloaded from USGS I have peak values of some. they do not match. I am not sure if fft helps or not.

[Walter Roberson]

trapazoid rule is about the best numeric integration you can get when you do not have a model function. Earthquake movement studies have developed some model functions, and so can improve on trapazoid rule in some cases.