Suppose functions $f(x)$ and $g(x)$ are continuous on the finite interval $a,b,ab,$ and ${\displaystyle \underset{a}{\overset{b}{}}}[f(x)+g(x)]dx=0.$ Then

$($Choose all the correct statements below$)$

$($A$){\displaystyle \underset{b}{\overset{a}{}}}[f(x)+g(x)]dx=0.$

$($B$)$ If $f(x)=(x^2-1)$ and $g(x)=(2-x^2),$ then ${\displaystyle \underset{a}{\overset{b}{}}}[f(x)+g(x)]dx=0$

$($C$){\displaystyle \underset{a}{\overset{b}{}}}[f(x)-g(x)]dx=-2{\displaystyle \underset{a}{\overset{b}{}}}g(x)dx$

$($D$)f(x)+g(x)=k,$ where $k$ is a constant not equal to zero.

$($E$){\displaystyle \underset{b}{\overset{a}{}}}[f(x)+g(x)]dx0.$

${\displaystyle \underset{a}{\overset{b}{}}}f(x)dx=-{\displaystyle \underset{a}{\overset{b}{}}}g(x)dx$

For any point $c,$ where $a$