integrate { 2x- [2x] }^2 ,limit 0 to 100[x] ,where [.] is G.I.F

0^100[x] ∫( fraction part 2x)^2dx

let 2x=t

   2dx=dt

  dx=dt/2          x=0 ;t=0

                       x=100[x] ;t=200[x]

0^200[x] ∫{t}^2 dt/2 

(period of fraction part is 1)

200[x]*0^1∫t^2dt/2  = 100[x]/3