Let f : [0,1] → R be a function defined by:
f(x) = \begin{cases} 0, & \text{if 0 ≤ x < 1} \\ 1, & \text{if x = 1} \end{cases}
Proof f is Riemann integrable on [0,1] using L(Pn) and U(Pn)
Now I try and attempts to show The suprema of L(Pn) is equal to the infimum of U(Pn). I found U(P) to be 1/n and L(P) = 0 so by letting n → ∞ we can deduce L = U. Is this approach i took correct?