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.

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