Construct a sequence of functions \(\left(u_{n}ight)_{n \in \mathbb{N}}\) which are Riemann integrable but converge to a limit \(u_{n} ightarrow u\) which is not Riemann integrable.

[ consider e.g. \(u_{n}=\mathbb{1}_{\left\{q_{1}, q_{2}, \ldots, q_{n}ight\}}\), where \(\left(q_{n}ight)_{n}\) is an enumeration of \(\mathbb{Q}\).]