Ans would be D.

(A) both integers are even - Not necessary. Nos can be 1 and 5
(B) both integers are odd - Not necessary. e.g. 4,2
(C) both integers are positive - Not necessary e.g. -1, 7
(D) if one integer is negative, the other is positive - - TRUE - since the sum of 2 nos are positive. So, if one no is negative then the other no has to be +ve for sum to be positive.
(E) if one integer is positive, the other is negative - Not necessary. 5, 1. OR 4, 2. This condition will be true only when first no is greater than 6

Hope this clears your doubt

D for me too. No other option restricts the choice of second integer.

As usual, Kajcha has given a very good explanation of this question. Yop! The OA is correct and Kajcha has already explained that! But Crackitpal, request you when you are providing the OA in ur post, please use the spolier - (button comes on the right under the Subject textbox.)

Thank you kajcha, got it !

camitava, I'll use spoiler from now on... Thanks !