solve symbolic integral for special case values (extract domain from solution?)

I am trying to take the definite integral of a symbolic function with an extra free variable (ie there's an unknown integer constant k in ). Using int(f,t,a,b) directly gives me a piecewise solution undefined at k=3, but if I use subs(f, k , 3) before integrating I get a valid solution. I know that if I have the solution I can combine it using piecewise, but I'd like to be able to do it more generally.

Is there a way to automatically detect the missing values of k so I can loop over them and add them to the general solution? It would appear to be possible from the defintion of the underlying Mupad object, but I don't know how to get at that from the matlab function.

Better yet, is there a way to force the int function to do that itself?