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Does it make sense to talk about the area of the region {(x,y)|x[itex]\in[/itex][a,b];y[itex]\in[/itex][0,f(x)]} for a positive function f defined on an interval [a,b], where a,b[itex]\in[/itex]ℝ and f is integrable on that interval, even if the function is not continuous?

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