$f: [0,1] \to \mathbb{R}$ where
\begin{equation} f(x)= \begin{cases} 4x^3 & \text{if } x \in \mathbb{Q}\\ 0 & \text{if } x \in \mathbb{R}\setminus\mathbb{Q} \end{cases} \end{equation}
Here, it is easy to argue $L(f;p) = 0$ hence $L(f) = 0 $ how do I evaluate the upper Riemann sum, hence the upper Riemann Integral?
Here given any $K^{th}$ subinterval $U(f;p) $ depends on the $p$ partition right? because there exist an irrational number in $K^{th}$ sub interval such that $U(f;p) > 0$ but I can't make the flow of the proof there rigorously.