Isn't the data insufficient?

Calculus Level 4

If \(f(x)\) is a function satisfying \( f(x+25) + f(x) = 0\) for all \( x \in \mathbb R\) such that,

\[\int_{b}^{c+b} f(x) \ dx\]

is independent of \(b\), then find the least positive value of \(c\).

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