Hello from MrBillDoesMath! 
 
 
Answer: 
 -15, -14
Discussion: 
Let "n" be the first of the two consecutive integers . Per the Question
n + (n+1) = -29 =>
n + n + 1 = -29 =>
2n +1 = -29 =>
2n = -29 -1 =>
2n = -30 =>
n = -15, 
Hence n = -15 and n+1 = -15 +1 = -14
Thank you, 
 
MrB