Question: **Real Analysis** Let (f) be a real-valued function defined on ([0,1]) that is Riemann integrable. Prove that if a sequence of functions ({f_n}) converges uniformly

**Real Analysis** Let \(f\) be a real-valued function defined on \([0,1]\) that is Riemann integrable. Prove that if a sequence of functions \(\{f_n\}\) converges uniformly to \(f\) on \([0,1]\) and each \(f_n\) is Riemann integrable, then \[\lim_{n\to\infty}\int_0^1 f_n(x)\,dx =\int_0^1 f(x)\,dx.\]

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