Here is my question:
Let $g(x)$ be the function defined on $[0, 2]$ such that $g(x) = 1$ for $0 ≤ x ≤ 1$ and $g(x) = 2$ for $1 < x ≤ 2$. Use the definition of the Riemann Integral to show that $g(x)$ is Riemann Integrable over the interval $[0, 2]$.
Also, is it necessary that the upper and lower Riemann sums converge to the same value? In an unrelated question, I evaluated an infinite sum corresponding to both limits and proved that they were not equal. By this fact alone, can I say that the said function was not Riemann Integrable?