From the information on topic - Integration of xmgrace,
... the item marked cumulative sum will construct a set composed of the current value of the integral at a given X. Sum only reports just the value on the next line. ...
I couldn't find information on the integration technique (Trapezoidal rule, Simpson's method ...) which thus motivates the question,
What numerical integration technique does xmgrace use to integrate the data sets chosen?
After downloading the latest xmgrace (a.k.a. Grace) source code I first searched through all files for the word "integration". I found a number of methods used for numerical integration. They all lead me to a function called trapint(), which is helpfully commented as shown:
/*
* trapezoidal rule
*/
It can be found in the file computils.c for anyone who wishes to investigate further.
Secondly, when I searched for "Simpson" I did not find anything.
According to this page, even MatLab does not have a built-in implementation of Simpson's method (I don't know how recent that page is, but I believe this is still true and couldn't find any other evidence of such a method). Therefore, I would not expect xmgrace to have one either, since it is a much smaller program with only a few contributors.
Also, if Simpson's method had been implemented in xmgrace in addition to the Trapezoidal rule method, there would surely be an option in the Transformations > Integration menu, so that users could choose which method they wanted.
All this evidence strongly suggests to me that xmgrace uses just the Trapezoidal rule for numerical integration. I hope this answer satisfies you.
