Visualization

Trace through an example. Array: $[2, 4, 1, 3, 5]$.

Building prefix sums:

$prefix[0] = 0$

$prefix[1] = 0 + 2 = 2$

$prefix[2] = 2 + 4 = 6$

$prefix[3] = 6 + 1 = 7$

$prefix[4] = 7 + 3 = 10$

$prefix[5] = 10 + 5 = 15$

Query: sum from index $1$ to $3$ (elements $4, 1, 3$).

Answer: $prefix[4] - prefix[1] = 10 - 2 = 8$. Check: $4 + 1 + 3 = 8$. It works.