Define f:[-2,2]---->R by

$\displaystyle f(x)=x^{2}$, x belongs to irrationals.

$\displaystyle f(x)=0$ otherwise.

Suppose P is a partition of [1,2].

i) Show that L(f,P)=0

f has infimum zero in any subinteral. Therefore L(f,P)=0 for any partition P.

ii) How do i show $\displaystyle U(f,P)\geq1$

do we just say f has supremum greater than 1 in any subinterval. Therefore $\displaystyle U(f,P)\geq1$ for any partion P.

iii) does $\displaystyle \int_{-2}^2f(x)dx$ exist?

Thank for any help.