F(x) is increasing function if F'(x) >=0 (non negative)
here F'(x) =-1/(1+x2) + 1
= x2/(1+x2)
which is always greater than or equal to 0 (means non negative)
becoz both x2 >=0 and (1+x2 ) > 0
(we know square of the number always non negative )
so here F(x) is increasing for all real number