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Three of these four hold for the definite integral. The exception is

  • A.it is a number rather than a function
  • B.it changes sign when the limits are exchanged
  • C.it depends on the constant of integration chosen
  • D.it is additive over adjoining intervals

Answer: C

The constant cancels in \( F(b) - F(a) \), so it cannot affect the value: this is precisely why a definite integral is well defined although the antiderivative is not unique. Additivity, being a number, and the sign change on exchanging limits are all genuine properties

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