Integrability

Calculus Level 1

$f(x)=\begin{cases} 0\text{ if } x\text{ is rational}\\\\ 1\text{ if }x\text{ is irrational} \end{cases}$

Is the function above Riemann integrable on $[0,1]?$
Is it Lebesgue integrable on $[0,1]?$