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δ(x) = 0 for all x ≠ 0

∞ for x = 0

∫_{-∞}^{∞}δ(x)dx = 1

I don't understand how the integral can equal unity. The integral from -∞ to zero is zero, and the integral from 0 to ∞ is zero. How can one integrate the discontinuity at zero to equal one? What am I missing? TIA for your insight.

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# I Question regarding the Dirac delta function

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