incorrect symbolic integral

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Ideas?

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Yes, please specify your question in more detail and attach your worksheet and tell us which version of Prime you are using.

In particular, you would have to explain why you believe that Prime's result is “incorrect”!
The quality and performance of the symbolics in Prime is far below that of Maple or Mathematica and so Prime is very often not able to deliver results or simplify them in a desirable way.

Prime seems to think that f and f2 are identical even its not capable enough to simplify f2 accordingly,

Let's test both functions using some random arguments:

Looks good and feeds the suspicion that Prime's integral might be correct after all, doesn't it?

Lets try using 100 000 sets of random arguments instead of just 3:

Only six times the values differ for more than 10^-5.

You have to decide if that's simply due to various numerical inaccuracies/round-off errors or if it means that Primes integral/derivative are incorrect.

Recalculation of the sheet generates different random numbers and I got up to 26 values out of 100 000 with a difference greater than 10^-5.

Prime 11 sheet attached