If \[\mathbf{m}\text{ }+\text{ }\mathbf{1}\] and \[\mathbf{n}\text{ }-\text{ }\mathbf{1}\] are integers then which of the following may not be an integer?

• A. \[\left( m+n \right)~\]
• B. \[\left( m\text{ }+\text{ }5 \right)\text{ }-\text{ }\left( n\text{ }+\text{ }2 \right)\]
• C. \[\left( m-3 \right)\,\,\div \,\,\left( n+4 \right)~\]
• D. \[\left( m\text{ }+\text{ }2 \right)\times \left( n\text{ }-\text{ }3 \right)\]
• E. None of these