Apologies to whoever posted this, whose identity I've forgotten: << When I participated in Maple beta program, I submitted this bug. It was a heated discussion there about it, and I was told by Maple developers that in Maple indefinite integrals are defined up to "a piecewise constant", i.e. integrals of continuous functions can be discontinuous. The bug was classified as "works as designed".
I find this philosophy rather ridiculous for antiderivatives of continuous functions. But for antiderivatives of functions continuous but on natural domains that are not connected, like the ubiquitous f(x) = 1/x, calculus books should give its antiderivative as ln|x| + C_1, x > 0 F(x) = { ln|x| + C_2, x < 0 for arbitrary choice of constants C_1, C_2, and likewise for 1/x^p, p > 0, p <> 1 (and mutatis mutandum for sec(x), csc(x), etc.). --Dan