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Found problems: 1

1986 Traian Lălescu, 2.3
Tags: function , calculus , derivative , integrals , FTC , Rolle's theorem , inequalities
Let $ f:[0,2]\longrightarrow \mathbb{R} $ a differentiable function having a continuous derivative and satisfying $ f(0)=f(2)=1 $ and $ |f’|\le 1. $ Show that $$ \left| \int_0^2 f(t) dt\right| >1. $$