Struggling to understand a concept.

[Ethan3141]

I read somewhere that a function being R-integrable doesn't imply that the function has an anti-derivative. I was wondering (assuming this is true and I recalled it correctly) if someone could help me understand it. I have been trying to think of counter examples but I can only seem to find ones in the other direction. Any help will be appreciated, thanks.

 

[Steven G]

Consider f(x) = 0, -1<x<0
1, 0<x<1

 

[Ethan3141]

Consider f(x) = 0, -1<x<0
1, 0<x<1

Oh my god, wow this makes it look so easy, I am ashamed I couldn't think of a counter example now :/

Thanks for the help