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Question Number 120089 by ZiYangLee last updated on 29/Oct/20

$$\mathrm{If}\mathrm{a}\mathrm{continuous}\mathrm{function}f:\mathbb{R}\to \mathbb{R}\mathrm{satisfies}$$$${\int }_0^{1}f\left(x\right)dx={\int }_0^{1}xf\left(x\right)dx=1$$$$\mathrm{prove}\mathrm{that}{\int }_0^1{\left(f\left(x\right)\right)}^{2}dx⩾4$$

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