Limits of integration on density of states in semiconductor

The density of electron states in a 3D semiconductor is given by $rho(E)=frac{1}{2pi^2}left(frac{2 m^*}{hbar^2}right)^{3/2}sqrt{E}$, derived commonly as shown here. I’m trying to understand how to set $E$ when I’m counting states, thinking in terms of a band diagram like this one.

If I’m counting the number of states between the bottom of the conduction band (maroon) and 150meV above the bottom, I think I can rationalize the integral running from 0 to 150meV, as the bottom of the conduction band is the lowest energy in that particular E-k relation. But by that same logic, if I was counting states from 150meV down into the valence band (light blue), I’d expect the integral to run from -150meV to 0meV, or even something like 139.850meV to 140meV, which seems off based on discussions with my instructor. A negative energy in the density of states doesn’t make sense to me, as that would mean an imaginary density of states. But I can’t figure out how to rationalize the integral running from 0meV to 150meV in that case, as that "150meV" is actually lower energy than "0meV". What are the proper limits of integration for these two cases, and how can I understand that?