The Riemann integral of f equals S if the following condition holds:
For all ϵ>0, there exists a δ such that for any tagged partition x0,…,xn and t0,…,tn−1 whose mesh is less than δ, we have ∣i=0∑n−1f(ti)(xi+1−xi)−S∣<ϵ
Note: The Riemann integral of f equals S if the following condition holds:
∀ϵ>0, ∃δ such that for any tagged partition x0,…,xn and t0,…,tn−1 whose mesh is less than δ, we have i=0∑n−1f(ti)(xi+1−xi)−S<ϵ.
Inspiration.
The correct answer is: Does not exist
Riemann-Lebesgue criterion
The function f:[a,b]→R is Riemann integrable if and only if (it is bounded and the set of points at which it is discontinuous has Lebesgue measure zero).