I'd love your help with proving that for $f:[0,1] \to \mathbb{R}$ monotonically decreasing function ,for every $\alpha \in (0,1)$ :$\int_{0}^{\alpha} f(x)dx \geq \alpha\int_{0}^{1}f(x)dx$. I tried couple of inequalities but I didn't conclude what I should.
Thanks a lot.