Question: Please help me out with this, thanks! (7) Prove the sequential criterion for integrability: for a bounded function f : a, b - R, if

Please help me out with this, thanks!

(7) Prove the "sequential criterion for integrability": for a bounded function f : a, b - R, if there is a sequence of partitions (P. )p n=1 satisfying lim U(f, Pn) - L(f, Pn)] = 0, then f is integrable on [a, b] with [" f = lim, . U(f, P,) = lim,- L(f, P.)

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