Another Functional Equation

Calculus Level pending

Let \(f : \mathbb{R} \rightarrow \mathbb{R^+}\) be a function with the following property -\[f(x)=\int_{0}^{x} \left[t-f(t)\right] \ \mathrm{d}t\]

If \(f(0)=0\), then find \[\lfloor 100f(1) \rfloor\]

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