Consider the inner product $\langle p(x),q(x)\rangle:=\int_0^1 p(x)q(x) dx$ on the vector space $V$ of real polynomials with degree less than 2. The linear functional $f:V\to \mathbb {R}$ is defined by $f(p(x))=p'(-12)+1 p(-3)$. According to the Riesz Representation Theorem, there is an $r(x) \in V$ such that $f(p(x)=\langle p(x),r(x) \rangle$ for all $p(x)\in V$. Find this $r(x)$.
$r(x) =$