Using right hand end points to evaluate integral

Question

Use definition ∫(from a to b) f(x)dx=lim(n to ∞)∑f(x₁) delta x. With values n above ∑ and i=1 underneath.

Problem: Use right hand end points to evaluate integral

∫( from 1 to 2) (x²+1)dx

Answer 1

∫( from 1 to 2) (x²+1)dx

∫ (x²+1)dx from 1 to 2 = x³/3 + x = 2³/3 + 2 - (1³ + 1) = 3.3333