Calculus
# Antiderivatives

If $a ,b,$ and $c$ are constants satisfying $\int \left( 12x^3 +ax-9\right)dx=bx^4+3x^2+cx+C,$ what is the value of $a+b+c?$

**Details and assumptions**

$C$ is the constant of integration.

If $f(x)$ satisfies $\int (2x+1)f(x)dx = x^4-2x^3-2x^2+C,$ what is the value of $f(5)?$

**Details and assumptions**

$C$ is the constant of integration.