INTEGRAL BY WAY OF INFINITE PARTITIONS

We propose a new form of integral which arises from infinite partitions. We use upper and lower series instead of upper and lower Darboux finite sums. We show that every Riemann integrable function, both proper and improper, is integrable in the sense proposed here and both integrals have the same value. We show that the Riemann integral and our integral are equivalent for bounded functions in bounded intervals.