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All I know is that it uses the fundamental theorem of calculus.

$$\large\frac{d}{dx}\int_{x^2}^{\sin x} e^{xt^2}dt = e^{x\;\sin^2 x}\cos x - e^{x^5}2x+\int_{x^2}^{\sin x} t^2e^{xt^2}dt$$

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    Zev Chonoles, thanks for the edit. I have to learn how to write those formulas.2012-01-16

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