Let$$f(\theta )=\sum _{0\le k\le n}{c}_k{e}^{ik\theta }$$be a trigonometric polynomial all of whose roots are real, such that ${\max }_{\theta \in [0,2\pi ]}|f(\theta )|=1$. Then$${\int }_0^{2\pi }|f(\theta )|\mathrm{d}\theta \le 4.$$