I'm no good at coming up with examples... please help...

a. Give an example of a function f: [0,2] $\displaystyle \rightarrow$ R such that f isn't Riemann integrable on [0,2], but |f| is.

b. Give an example of a function f: [0,2] $\displaystyle \rightarrow$ R such that f isn't Riemann integrable on [0,2], but $\displaystyle f^2$ is.

c. Give an example of two functions f,g : [0,1] $\displaystyle \rightarrow$ R such that f is Riemann integrable on [0,1], but g isn't and fg is Riemann integrable on [0,1].