Integrate

from 1 to 2.5        [ x ] dx             where [ ] is greatest integer function.

Try to analyze it's graph.

Check the graph on this link:

http://library.thinkquest.org/20991/alg2/graphs.html

now, u'll get to know that [x] is 1 for (1,2) and 2 for (2,2.5).

so, u'll get :

1.dx for (1,2) = 1

and 2.dx for (2,2.5) =1.

So, ans is 2.

Do ask again if any doubt is there.

This is the graph of greatest integer function (or the floor function).

Now break the limit for the integral first from 1 to 2 and then from 2 to 2.5.

I = int x from 1 to 2.5 [x] . dx

I = int x from 1 to 2 [x] . dx + int x from 2 to 2.5 [x] . dx

I = int x from 1 to 2 (1) . dx + int x from 2 to 2.5 (2) . dx

I = limit from 1 to 2 (x) + limit from 2 to 2.5 (2x)

I = (2 - 1) + 2(2.5 - 2) = 2 (Ans)