Uniform limits of Riemann integrable functions are Riemann integrable

Define precisely the notion of Riemann integrability for a function \(f ( x )\) on [0, 1].

Suppose that \(f _ { n } ( x )\) is a sequence of Riemann integrable functions on [0, 1] such that \(\{ f _ { n } ( x ) \}\) converges uniformly to \(f ( x )\) . Prove that \(f ( x )\) is Riemann integrable.