I have 

integration of  [ t³-1+tcos t  ] dt

with limits -1 to +1.

Dunno about your problem but the Greatest integer function cannot be split.

For e.g.- [x + x⁵]  is not equal to [x] + [x⁵] at at least one point  x= 3/2.

Dunno about your problem but the Greatest integer function cannot be split.

For e.g.- [x + x⁵]  is not equal to [x] + [x⁵] at at least one point  x= 3/2.