Problem $1.$ Find the area which is shown in the following graph and lies between $f(x)=-\frac{1}{2}{x}^2-\frac{7}{2}x+4$ and $g(x)=\frac{3}{2}x+12.$

Problem $2.$ Given the following ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}f(x)dx=3ln(x)+c,{\displaystyle \underset{-1}{\overset{3}{}}}g(x)=-5,{\displaystyle \underset{12}{\overset{-1}{}}}g(x)=9,h^{\text{'}}(x)=e^x.$ Find:

$1-{\displaystyle \underset{3}{\overset{12}{}}}g(x)$

$2-f(e^2)$

$3-h(x)$ if you know that $h(0)=4$

$4-{\displaystyle \underset{-1}{\overset{12}{}}}(f+g)(x)$ if you know that $c=0$