hey toshi ,

             look,

in any question of greatest integer , discontinuity lies at INTEGER ...(RIGHT)............

NOW FOR x^{2    , discontinuity will lie at}

  s

     2  ,  3,    4  ,    5,   6  ,  7  ,   8  ,   9     ( upto x=3)

now this is same 4 [x² +1 ]................. bcoz fact remains same.....................here also x2 will be considered...................therefore from

X=1  TO X=3...........WE GET 8 VALUES  ( U CAN COUNIT )...

THANKU