Question

Two consecutive integers have sum of 137

Answer 1

You would do x+ (x+1)=137
2x+1=137
Subtract 1 from each side
2x=136
x=68.
Add 1 to 68, since they are consecutive integers.
The answer is 68 and 69 

Answer 2

Here's how you approach a problem of this nature in general:
Let x be the lower of the two integers.
Then (x+2) is the other integer
and x+(x+2) = 137
2x + 2 = 137
2x = 135
x = 67.5 - which isn't an integer, of course, but we already knew there was no solution to this problem!