EDB — 19Q

[19Q] Note:Similar to point [8]↺↻ from exercise [1J3]↺↻.Suppose $f_n:[a,b]\to ℝ$ are Riemann-integrable, and $f:[a,b]\to ℝ$ a generic function.

Find an example where $f_n{\to }_{n}f$ pointwise, $f$ is bounded, but $f$ is not Riemann integrable.

Show that, if the convergence is uniform, then $f$ is Riemann integrable and