Integrate question

[Arno K]

Just my 2 pence, aren't you discussing different things? The one is integration by CAS machines and by hand where some obviously identical but different looking antiderivatives were produced, here any constant added would not change the result, to fulfill anybodies needs CAS could add something like @Cn add the end.
The other is then transforming one antiderivative into another, transformations using identities wth trig functions always involve constants being added or subtracted, these cannot be omitted, otherwise the functions written would be different.
But, and this is my point of view, anybody using a machine to perform some task for him should know what he/she is doing, be able to do it by hand and to check different looking results for equivalence.