Okay integers are numbers that can be written without a fractional component. It can be positive or negative numbers.
decimals, numbers with exponents or numbers with roots(square root or cube root etc) are not integers.
While consecutive means continuously or successively.
So for your question:
What are the sum of three consecutive integers?
Let's try this:
1 + 2 + 3 = 6 -> this one is a positive even integer
2 + 3 + 4 = 9 positive odd integer
-1 + 0 + 1 = 0 -> an integer (though some mathematicians have some argument if they should consider zero(0) an integer or not)
-3 + - 2 + -1 = -6 -> negative even integer
-4 + -3 + -2 = -9 -> negative odd integer
Result that consist of (1, 2, 3, 4 ...) are natural numbers also called whole numbers while (-1, -2, -3, -4 ...) are their additive inverses and zero(0) is simply zero.
As you have noticed the result can be positive or negative and odd or even but they are all just integers.
I'm not sure if your question was incomplete but i hope it helps.