For each function, state whether it is (i) bounded and piecewise monotonic; (ii) piecewise continuous; (iii) integrable on the domain given. No justification needed.
(a) $f: [-1,1] \to \mathbb{R}$, $f(x) = |x|$
(b) $f: [-1,1] \to \mathbb{R}$,
$f(x) = \begin{cases} \frac{1}{x^2} & x \neq 0\\ 0 & x = 0 \end{cases}$
(c) $f: [0,1] \to \mathbb{R}$,
$f(x) = \begin{cases} \frac{1}{n} & x \in (\frac{1}{n+1}, \frac{1}{n}] \text{ for } n \in \mathbb{N} \\\ 0 & x = 0 \end{cases}$
(d) $f: [0,1] \to \mathbb{R}$,
$f(x) = \begin{cases} x \sin(\frac{1}{x}) & x \neq 0 \\\ 0 & x = 0 \end{cases}$
