let the first integer is X

so, next consecutive integer will be = X+2

from ques, we have  (X+2)^2- X^2 = 6

i.e, x^2+4+2x=6

or, x^2+2x-2 =0

or,(x-1)*(x-1)=0     -- breaking this into factors

i.e, x=1, and x+2 =3.

therefore (1,3) are two such consecutive odd nos.