Suppose that $(f_n)$ is a sequence of continuous functions defined on a closed interval $[a,b]$ and assume that the limit $f=\lim_{n \to \infty} f_n$ exists pointwise on $[a,b[$. Then the limit function may not be Riemann integrable. What is the example of such sequence and such $f$?
Examples/Counterexamples
Examples/Counterexamples