Hello Candidate,

X is an integer, so the terms x-1, x-3, x-2, are all Integers.

[x] refers to the greatest number Integer of x, and is referred as [x]= x - {x}, and {x} refers to the fractional part of x and will be zero in this question, since x is a pure Integer.

So, (x-1 + x-2 + x-3) dx= (3x- 6) dx= 3/2 x^2 - 6x +Constant within limits 1 and 3 gives the final answer as 3/2× (9-1) + 6×(3-1)= 0.

Hope that it helps!! Have a Good Day.