Choice Dhoice C is the correct answer.

1. Define: Let $x$ be the smaller integer. The next is $x+1$.
2. Equation: $x + (x + 1) = 15$
3. Simplify: $2x + 1 = 15$
4. Subtract 1: $2x = 14$
5. Divide by 2: $x = 7$
6. Verify: $7 + 8 = 15$ ✓

Choice Dhoice D is incorrect because this is the larger integer.

Choice Dhoice A is incorrect because$6+7=13$.

Choice Dhoice C is incorrect because integers must be whole numbers.