Solution
Let the integers be n and (n+1)
[tex]\begin{gathered} n(n+1)=42 \\ \\ n^2+n=42 \\ \\ n^2+n-42=0 \\ \\ (n+7)(n-6)=0 \\ \\ n=-7,6 \end{gathered}[/tex]Therefore, the answer is
[tex]\begin{gathered} 6\text{ }and\text{ }7 \\ \\ or \\ \\ -7\text{ }and\text{ }-6 \end{gathered}[/tex]