Application of Gronwall's lemma (square function)

Question

I wanna use Gronwall's lemma to this inequality: $$\frac{d}{dt}f(t)^2\leq A(t) f(t)$$ I thaught of using $ab \leq a^2+b^2$ then we'll have: $$\frac{d}{dt}f(t)^2\leq A(t)^2+ f(t)^2$$ But how can I use the Gronwall's lemma in this case