functional minimization problem

Question

Let $f:[0,1]\to [0,1]$. Define $\|f\|_1=\int_0^1f(x)dx$ and $\|f\|_2=\sqrt{\int_0^1(f(x))^2dx}$.

How to find a $f$ such that $\frac{1-a\|f\|_1+\frac{(b\|f\|_2)^2}{2}}{b\|f\|_2}$ is minimized? ($a\in \mathbb{R}, b\geq0$)