what is the integrand of [x2-1] upperlimit-2,lower limit-0 where [ ] represents greatest integer function

From the graph , y+1 = x2 , we can say

between x=(0,1)  y takes value of -1

x=(1,1.414)        y takes value of 0

x=(1.414,1.732)  y takes value of 1

x=(1.732,2)        y takes value of 2

integrating in these limits gives

I = int ( -dx) + int ( 0*dx) + int ( dx) + int ( 2*dx) with above limits respecively

I = 1.732 - 1.414 = 0.218

--

regards

Ramesh

graph of [x^(2)-1]

integration is the area under the graph so its basically the area of the rectangle tht is 1*-1=1