Step in Proof at the beginning of Gelfand and Fomin's

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In the proof below (from Gelfand and Fomin's Calculus of Variations), how exactly is Taylor's Theorem used to derive the equality $$\triangle J = \int^b_a[F_y(x,y,y')h+F_{y'}(x,y,y')h']dx + \dots?$$

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