# Integrability

Calculus Level 2

Is the function $f(x)=\begin{cases} 0\text{ if } x\text{ is rational}\\ 1\text{ if }x\text{ is irrational} \end{cases}$ Riemann integrable on $$[0,1]$$? What about lebesgue integrable on $$[0,1]$$?

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