Suppose that \( f: [a, b] \to \mathbb{R} \) is a smooth, convex function, and there exists a constant \( t>0 \) such that \( f'(x) \geq t \) for all \( x \in (a, b) \). Prove that

\[

\left| \int_a^b e^{i f(x)} dx \right| \leq \frac{2}{t}.

\]

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