This kind of problem always seems like it's a bit confusing, but there's a trick that works.
We can use the letter x to stand for the smallest of the three numbers. Since the three integers are consecutive, the second smallest number must be x + 1 and the third smallest (largest) number must be x + 2.
Since all three of the numbers add up to 30:
x + (x + 1) + (x + 2) = 30