# Math Help - Examples of Riemann integrable functions

1. ## Examples of Riemann integrable functions

a. Give an example of a function f: [0,2] $\rightarrow$ R such that f isn't Riemann integrable on [0,2], but |f| is.
b. Give an example of a function f: [0,2] $\rightarrow$ R such that f isn't Riemann integrable on [0,2], but $f^2$ is.
c. Give an example of two functions f,g : [0,1] $\rightarrow$ R such that f is Riemann integrable on [0,1], but g isn't and fg is Riemann integrable on [0,1].
2. Let $f(x)= 1$ if $x\in \mathbb{Q}$ and $f(x)=-1$ if $x\in \mathbb{R} \setminus \mathbb{Q}$ and $g\equiv 0$