Integrals Problem

Question

The interval [0,4] is partitioned into n equal subintervals, and a number xi is arbitrarily chosen in the i^th subinterval for each i. Then:

lim (n→∞) n ∑ i=1 [(2xi+3)/n] = ?

Answer 1

im (n→∞) n ∑ i=1 [(2xi+3)/n] = ∫₀⁴(2x + 3)/4dx = (x² + 3x)/4₀⁴ = 7