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

Let ${\displaystyle {}I}$ be a real interval and let
${\displaystyle f\colon I\longrightarrow \mathbb {R} }$
be a continuous function with antiderivative ${\displaystyle {}F}$. Let ${\displaystyle {}G}$ be an antiderivative of ${\displaystyle {}F}$ and ${\displaystyle {}H}$ an antiderivative of ${\displaystyle {}G}$. Let ${\displaystyle {}a,b,c\in \mathbb {R} }$. Determine an antiderivative of the function
${\displaystyle (at^{2}+bt+c)\cdot f(t).}$