\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Show that the function \(F\) defined by \(F(x) = \dfrac{1}{3}(x+1)^3\) is an antiderivative of \(f(x) = (x+1)^2\) on \(\mathbb{R}\).
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