If f and g are defined as f(x) = f (a -x) and g(x) + g (a -x) = 4, then ${\int }_0^{\mathrm{a}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{g}\left(\mathrm{x}\right)\mathrm{dx}$ is equal to

• A

  ${\int }_0^{\mathrm{a}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}$

• B

  $2{\int }_0^{\mathrm{a}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}$

• C

  $2{\int }_0^{\mathrm{a}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{g}\left(\mathrm{x}\right)\mathrm{dx}$

• D

  None of these