Explanation:

Let the two consecutive positive integers be X and (X + 1).
X^2 + (X+1)^2 - X(X+1) =91
X^2 + X -90=0
(X+10) (X-9)=0
X= -10 or 9
As X is positive x =9 
Hence the two consecutive positive integers are 9 and 10.