Let $f_n$ be a sequence of differentaible functions on $[0,1]$ to $\mathbb{R}$ converging uniformly to a function $f$ on $[0,1]$, Then
$f$ is differentiable and Riemann integrable there
$f$ is uniformly continuous and R-integrable
$f$ is continuous, need not be differentiable on $(0,1)$ and need not be R-integrable on $ [0,1]$,
$f$ need not be continuous.
Well I think 2 is only correct statement as every $f_n$ are differentiable on $[0,1]$ hence uniformly contnous, and as they converge uniformly to $f$ on $[0,1]$ so $f$ is uniformly continuous and every continuous function is rieman integrable..Am I correct?