Let a be a positive real number. For every second-degree polynomial $P ( x )$ with real coefficients and leading coefficient 1,
$$\int _ { - 1 } ^ { 1 } \mathrm { P } ( \mathrm { x } ) \mathrm { dx } = \mathrm { P } ( \mathrm { a } ) + \mathrm { P } ( - \mathrm { a } )$$
the equality is satisfied.\\
Accordingly, what is the value of a?\\
A) $\sqrt { 2 }$\\
B) $\sqrt { 3 }$\\
C) $\sqrt { 6 }$\\
D) $\frac { \sqrt { 2 } } { 2 }$\\
E) $\frac { \sqrt { 3 } } { 3 }$