[tex]\int 6x+18\, dx=3x^2+18x+C\\\\
3=3\cdot 1^2+18\cdot1+C\\
3=3+18+C\\
C=-18\\
f'(x)=3x^2+18x-18\\\\
\int 3x^2+18x-18\, dx=x^3+9x^2-18x+C\\\\
5=1^3+9\cdot1^2-18\cdot1+C\\
5=1+9-18+C\\
C=13\\\\
f(x)=x^3+9x^2-18x+13
[/tex]
[tex]f(-2)=(-2)^3+9\cdot(-2)^2-18\cdot(-2)+13\\
f(-2)=-8+36+36+13\\
\boxed{f(-2)=77}[/tex]
But honestly I don't know if it's good method.
