To find the integer that makes the addition sentence true, we can set up the equation as follows:
\[ -17 + x = -19 \]
To solve for \(x\), we can add 17 to both sides of the equation:
\[ x = -19 + 17 \]
Calculating the right side gives:
\[ x = -2 \]
So, the integer that makes the addition sentence true is:
\[ \boxed{-2} \]