Question: If f R[a, b] and c R, we define g on [a + c, b + c] by g(y) := f(y - c).

If f ∈ R[a, b] and c ∈ R, we define g on [a + c, b + c] by g(y) := f(y - c). Prove that g ∈ R[a + c, b + c] and that ∫b+ca+c g = ∫ba f . The function g is called the c-translate of f.

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