I am solving old comprehensive real analysis exams and there are two questions that I can not be sure,
If $f$ is Riemann integrable then $|f|^r$ is Riemann integrable for any $r>0$.( True or False) I feel it is wrong indeed but couldnt find any example)
$1<p<q<r<\infty$, any function $f$ is in $L^q$ but not in $L^p$ and not in $L^r$.
Thank you for any help.