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Let \(\displaystyle{f:\mathbb{R}\longrightarrow \mathbb{R}}\) be a continuous function such that $$\int_{0}^{x}f(t)\,\mathrm{d}t>\int_{x}^{1}f(t)\,\mathrm{d}t\,\,,\forall\,x\in\left(-\infty,0\right)\cup\left(0,1\right)\cup\left(1,+\infty\right) $$. Prove that \(\displaystyle{\int_{0}^{1}f(t)\,\math...