Let $f_n$ and $f$ be continuous functions on an interval $[a, b]$ and assume that $f_n\to f$ uniformly on $[a, b]$. Pick out the true statements:
(a) If $f_n$ are all Riemann integrable, then $f$ is Riemann integrable.
(b) If $f_n$ are all continuously differentiable, then $f$ is continuously differentiable.
(c) If $x_n\to x$ in $[a, b]$, then $f_n(x_n)\to f(x)$.