Other half of Gronwall

Question

I am looking to show that if y(t) is continuous on (a, b) and satisfies

$$y(t)\leq H+K\int_{t}^{t_{0}} y(s)ds,\quad\forall\ a<t\leq t_0$$

where $t_0 \in (a,b)$, then

$$y(t)\leq He^{K(t_0-t)},\quad\forall\ a<t\leq t_0$$