Answer the following True or False.

If $\displaystyle {f{{\left({x}\right)}}}$  and $\displaystyle {g{{\left({x}\right)}}}$  are either both odd or both even functions and if

      $\displaystyle {\int_{{-{a}}}^{{a}}}{\left({f{{\left({x}\right)}}}-{g{{\left({x}\right)}}}\right)}{\left.{d}{x}\right.}$ 

gives the area between $\displaystyle {y}={f{{\left({x}\right)}}}$ and $\displaystyle {y}={g{{\left({x}\right)}}}$ for $\displaystyle -{a}<{x}<{a}$ then

      $\displaystyle$ $\displaystyle {2}{\int_{{0}}^{{a}}}{\left({f{{\left({x}\right)}}}-{g{{\left({x}\right)}}}\right)}{\left.{d}{x}\right.}$ 

also gives the same value.