Talk:Sum rule in integration

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This whole article needs to be rewritten. The fact that integration is a linear operator holds in quite general contexts, e.g. piece-wise continuous functions, or even non-continuous functions in the context of the Lebesgue integral. This "proof" only proves it for the very special case when the integrand is differentiable, this is a really small class of functions. Moreover, the "reason" why integration is linear doesn't really rely on FTC or the linearity of differentiation. This article gives the impression that the property only holds for diffable funcs.

It would be more appropriate to direct this comment at linearity of integration, rather than at this page that derives a basic rule from the antiderivative.

Charles Matthews 11:51, 14 Oct 2003 (UTC)