@MichaelE2 Only the complex answer is wrong, no? The first I interpret as "Integrate from exactly zero to some different number very very close to zero", and the answer is some number very close to zero. The last one I read as: "integrate from a not-precisely-defined number to exactly that same number", which is not number very very close to zero, but exactly zero.
@rhermans None of them are incorrect, are they? As for the precision in the last, your argument should apply to 1. - 1., since we're subtracting identical numbers; however, we get 0., not 0. The docs contain things like "When you do calculations with machine-precision numbers, however, the Wolfram Language always gives you a machine-precision result." Sometimes they hedge by including the word "typically."
The second integral, on the face of it, seems greater than the first. But the first is reported with a positive uncertainty and the second is an exact zero. I'm fine with it being some kind of zero. It seems less ok for a computation to shift from machine-precision to exact, though. Exact can be slow and hog memory.
