The bounded function f : (a, b) → R is Riemann integrable if and only if for every Є > 0 there exist a partition P [a, b] which may depend on Є , such that ______________. 

1
u(f;P) > L(f;P) 
2
u(f;p) - L(f;P ) < Є
3
u(f;P) - L(f;P) = 0 
4
u(f;P) - L(f;P) > Є

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