Finding the max of profit

Question

Is the following fourmula right when we have the MC and MR of a certain comodity ? $$P_{max}=\int_ 0^a (MR-MC)dx$$ where $a$ is the root of $MR(x)=MC(x)$ and $[MR-MC]'(a)<0$. I personally think that the lower band of the integral should be the least positive root of $TR(x) -TC(x)=0$. THANKS