integrals

[man111]

consider the differentiable function $f:\mathbb{R}\rightarrow\mathbb{R}$ for which $f(0)=0,f(1)=1$ and $\left|f^{'}(x)\right|\leq 2\forall x\in\mathbb{R}$ and possible values of $\displaystyle\int_{0}^{1}f(x)dx\in(a,b)$.Then $b-a=$ Where $a,b\in\mathbb{R}$

[zhoraster]

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