\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(f \in C([0, 1], \mathbb{R})\) with \(f \ge 0\) and \(\int_0^1 f(t)\,dt = 0\). Show that \(f \equiv 0\) on \([0, 1]\).
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