Give me a example of a function Lebesgue Integrable over [a,b] that is not bounded in any subinterval of [a,b] Give me a example of a function Lebesgue Integrable over [a,b] that is not bounded in any subinterval of [a,b]. 
*I'm thinking about this but without progress...

$f(x)=0,\ x\in{\Bbb R}\backslash{\Bbb Q}$
$f(r/s)=s$, $r/s$ irreducible fraction.
