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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §5.1 The Idea of the Integral, #4 · Calculus · Integrals

Any constant … can be added to the antiderivative … because the…

This problem is about sums $f_{j}$ and differences $v_{j}$ .

Any constant $C$ can be added to the antiderivative $f (x)$ because the ____ of a constant is zero. Any $C$ can be added to $f_{0}, f_{1}, \dots$ because the ____ between the $f$ 's is not changed.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §5.1 The Idea of the Integral, #4

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