Let f(x) is defined by f(x) = \(\begin{cases}x^2, x \text{ is rational}\\x^3, x \text{ is irrational}\end{cases}\) , x ∈ [0, 1]
1
f is Riemann integrable on [0, 1] and \(\int_0^a f(x)dx\) = 1/3
2
f is Riemann integrable on [0, 1] and \(\int_0^a f(x)dx\) = 1/4
3
f is not Riemann integrable on [0, 1]
4
none of the above