The Riemann integral is the sum of the area of rectangles as rectangle width goes to zero. So I assumed it was correct to say that "Riemann's definition starts with the construction of a sequence of easily-calculated areas (as opposed to integrals) which converge to the integral of a given function". I thought about this for a while and I guess you could say that your computing and adding integrals to get an integral, but it just does not seem logical to me. Please, I am merely an undergraduate, so if this is not the case please feel free to correct my blunder!
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