Integrability

Calculus Level 2

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

Is the function above Riemann integrable on \([0,1]?\)
Is it Lebesgue integrable on \([0,1]?\)

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