Question 59
For each positive integer $n$ the function $f_n : [0, n] \to \mathbb{R}$ is defined by $f_n(x) = \arctan(\lfloor x \rfloor)$. Prove that $f_n$ is a Riemann integrable function
and find
$$
\lim_{n \to \infty} \frac{1}{n} \int_{0}^{n} f_{n}(x) dx.
$$
and find
$$
\lim_{n \to \infty} \frac{1}{n} \int_{0}^{n} f_{n}(x) dx.
$$