I think the key word is continous. the RHS totally looks like a sum from a geometric series but I dont see a trick when I think there is one .
2026-03-31 21:52:00.1774993920
Integral that is continuous and looks like it converges to a geometric series
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Hint: Let $g(x) = (x+1)^{2017}$. Let $h = f-g$. By the mean value theorem, there exists $a$ such that $$h(a) = \int_0^1 h(x) \, dx.$$