From one to double integral inequality

Question

Let $f$ be a continuous function on $[0,1]$ and let $a\in (0,1)$. Prove that there exists a positive constant $c$ such that $$\int_a^1\int_{x-a}^xf^2(s)dsdx\geq c\int_0^1f^2(s)ds.$$ I cannot see how I can prove it. Any ideas guys?. Thank you.