A calculus problem by Abhinav Jha

Calculus Level pending

If $$F(x)$$ is a function satisfying $$F(x+a) + F(x) = 0$$ for all $$x\in \mathbb R$$ and a constant $$a$$ such that $$\displaystyle \int_b^{c+b} F(x) \, dx$$ is independent of $$b$$, then find the least positive value of $$c$$.

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