Can you think of a function that is neither improper Riemann nor Lebesgue integrable, but is Henstock-Kurzweil integrable?
I'd like to put a bounty on this question, but my reputation is not nearly enough yet. Translated to math, find $f$ such that
$ f \notin \mathscr{L,R^*} $ but $ f\in \mathscr{HK} $ where $\mathscr{HK}$ denotes the set of Henstock-Kurzweil integrable functions.