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I'm a complete n00b at calculus (first day of the first year) so this question may appear a little...stupid. But I want to hammer into my head every little thing I hear in the lecture hall, so I might as well give it a go.

Today the professor explained how jump discontinuities must be taken into consideration when determining the area under the curve using the limit of #of rectangles definition. I did not really understand, or at least as well as I would have liked. Basically I want to know why a function can be integrated only on a continuous interval, and not on an interval with a discontinuity in it.

Also, a function with a jump discontinuity is usually a piecewise defined function. Actually I think this isn't always so, as is the case with (x/|x|). Is it true that a piecewise defined function can't be integrated in one step, and each part has to be analyzed separately?

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# How are jump discontinuities important when determining the area of a curve?

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