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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