\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(f\) be defined on \(\mathbb{R}\) by \(f(x) = (x-1)e^{x^2-2x-2}\).
Determine the unique antiderivative \(F\) such that \(F(\sqrt{2}) = 1\).
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