Which of the following is true?
Let f: [0, 1] → R be defined by
f(x) = \(\rm \begin{cases} (-1)^{r-1}, & \rm when \frac{1}{r + 1} < x \leq \frac{1}{r}, r = 1, 2, 3,...\\ 0, & \rm when \ x = 0 \end{cases}\)
1
f is integrable on [0, 1], but f is unbounded
2
f is integrable on [0, 1]
3
f is not integrable in [0, 1]
4
f is not integrable on [0, 1], but not bounded