Let $f_n : [a,b] \to \mathbb{R}$ such that $f_n$ is uniformly convergent to $f$
and for every $n \in \mathbb{N}$, $f_n$ is not Riemann integrable on $[a,b]$
and the question asks whether $f$ is Riemann integrable on $[a,b]$ or not, under these conditions.
I think it's not integrable but I could not prove it, any help or hints ?!