If the sum of the first k positive integers is equal to, k(k+1)/2, What is the sum of the integers from n to m, inclusive, where 0<n<m?

A. (m(m+1)-(n-1)n)/2
B. (m(m+1)-(n+1)n)/2
C. (m(m-1)-(n-1)n)/2
D. (m(m-1)-(n+1)n)/2
E. (m(m+1)-(n-1)n)/4

OA is A

Why OA cannot be B

Suppose i need the sum of integers from 10 to 20. I will calculate the sum of (1 to 10) and subtract it from (1 to 20)

(sum of 1 to 20) - (sum of 1 to 10) = (sum of 10 to 20)

(m(m+1)-(n+1)n)/2 (where i am wrong)