Primitive function/f (at^2+bt+c) with primitive functions/Exercise

Let ${}I$ be a real interval and let

$f\colon I\longrightarrow \mathbb {R}$

be a continuous function with antiderivative ${}F$. Let ${}G$ be an antiderivative of ${}F$ and ${}H$ an antiderivative of ${}G$. Let ${}a,b,c\in \mathbb {R}$. Determine an antiderivative of the function

${\left(at^{2}+bt+c\right)}\cdot f(t).$

Create a solution