Given: ${\displaystyle \underset{a}{\overset{b}{}}}f(x)dx={\displaystyle \underset{c}{\overset{d}{}}}g(x)dx$

and the following statements:

The area between the $x-$axis and $f(x)$ from $x=a$ to $x=b$ is equal to the area between the $x$ axis and $g(x)$ from $x=c$ to $x=d.$

$f(x)$ from $x=a$ to $x=b$ is equal to $g(x)$ from $x=c$ to $x=d.$

Both $f(x)$ and $g(x)$ must be either totally above or totally below the $x-$axis.

${\displaystyle \underset{a}{\overset{b}{}}}f(x)dx-{\displaystyle \underset{c}{\overset{d}{}}}g(x)dx=0$

Only $1$ is correct.

Only $3$ is false.

Only $1)$ and $4)$ are correct.

All statements are true.