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**thaopanda** Determine whether the function f: [0,1] $\displaystyle \rightarrow$ R given by:

f(x):=

3 if $\displaystyle x \in Q \cap [0,1]$

1 if $\displaystyle x \in (R$ \ $\displaystyle Q) \cap [0,1] $

is Riemann integrable on [0,1].

I know that if it is Riemann integrable, sup L(P, f) = inf U(P,f), P being the partition of [0,1]

or $\displaystyle \int f(x)dx$ (lower integral of f over [0,1]) = $\displaystyle \int f(x)dx$ (upper integral of f over [0,1])

How do I show if it is or not?