If $f^{\mathrm{\prime }}\left(x\right)=g\left(x\right)$for $for a\le x\le b$ then ${\int }_a^b f\left(x\right)g\left(x\right)\mathrm{d}x$ is equal to

• A

  $g\left(b\right)-g\left(a\right)$

• B

  $f\left(b\right)-f\left(a\right)$

• C

  $\frac{\left(f\right(b){)}^2-(f\left(a\right){)}^2}{2}$

• D

  $\frac{\left(g\right(b){)}^2-(g\left(a\right){)}^2}{2}$