Is there a function f = g' but not Riemann Integrable
The second fundamental theorem of calculus states that:
If f is integrable in [a, b] and f = g' for some function g, then
so I was wondering if there is a function such that it is not Riemann integrable ( , or equivalent formulations), and f = g' for some function g.
Henstock-Kurzweil integral case
By any chance do you know Laurent, or any one else if that is also the case with the Henstock-Kurzweil integral (i.e. there's a function such that it is derivable, but it's derivative is not henstock-kurzweil integrable)?