Range Sum - Answering Queries

Once you have the prefix array, queries are trivial:

function sumRange(left, right):
    return prefix[right + 1] - prefix[left]

Time: $O(1)$. Space: $O(1)$ per query. The $+1$ offset handles the convention that $prefix[i]$ is the sum of elements before index $i$. If this feels awkward, trace through an example until it clicks.