so I have to prove that the signum function does not have an antiderivative on R.
I wrote the function down. Then took the integral of $1$ which was equal to $x$, $-1$, when $f(x)=-1$, and $C$, when $x= 0$. I really have no idea how to prove that a function does not have an antiderivative and I don't know what I'm doing. Could you please give some advice or show how I can solve this? Thank you very much.
P.S. Can a discountinous function have an antiderivative on R? I have just started learning about integration.