Provide an Appropriate Response $\mathrm { f } ( \mathrm { x } ) = \left\{ \frac { 1 } { \mathrm { x } } \right.$

Short Answer

Provide an appropriate response.
-A student wishes to take the integral over all real numbers of $\mathrm { f } ( \mathrm { x } ) = \left\{ \frac { 1 } { \mathrm { x } } \right.$ , if $x < 0 \frac { 1 } { \mathrm { x } ^ { 2 } }$ , if $x > 0$ and claims this is zero because $- \infty + \infty$ equals zero. What is wrong with this thinking?