# Unbounded and continuous almost everywhere

Can anyone give me an example of a function f:[a,b]->R which is continuous almost everywhere yet unbounded?

Thanks!

The function f:[0,1]->R given by
f(x) = n if x=1/n for some positive integer n
f(x) = 0 else

muchas gracias

Okay how about one which isn't Riemann (improper) integrable

$$\displaystyle\sum_{ k = 1 }^\infty k \chi_{ [ 0, \frac{ 1 }{ k^2 } ] }$$

matt grime