Prove/disprove:
1) If f has an anti-derivative in $[a,b]$ then $\int_a^b f(x)dx$ exists and is finite.
2) If $\int_a^b f(x)dx$ exists and is finite, then $f$ has an anti-derivative in [a,b].
Hello everyone, I'm quite baffled with anything that has to do with existence of an anti-derivative. I know that any function that has a removable or jump discontinuity point in some interval I then the function doesn't have an antiderivative at I. Would be happy to get some help on that question. Thanks in advance :)