Concept:The greatest integer function [x] is constant on every interval [n,n+1), so its integral is a sum of areas of rectangles.Explanation:Split the integral at the integer points x=1,2,3, since [x] changes value only at integers.∫0.23.5[x]dx=∫0.210dx+∫121dx+∫232dx+∫33.53dxEvaluate each constant piece:=0+1(2−1)+2(3−2)+3(3.5−3)=0+1+2+1.5=4.5Answer:4.5Hence, the correct option is C.