Both Ends Of The Range

Following the Competitive Programmer's Handbook convention, p[k] holds $a_0 + a_1 + \dots + a_k$, and $\text{sum}(a, b) = p[b] - p[a-1]$ with $p[-1]$ defined as 0.

Evaluate $\text{sum}(2, 5)$ and $\text{sum}(0, 2)$, in that order.