Problem involving second degree polynomial Let $ f : \bf R \to \bf R$ be a polynomial of the form $f(x)=a_0+a_1x+a_2x^2$,$a_2 \neq 0$.If $E_1= \int_ {-1} ^{1} f(x)dx -[f(-1]+f(1)]$,$E_2=\int_ {-1} ^{1} f(x)dx -\frac {1}{2} [f(-1]+2f(0)+f(1)]$ Then show that $\vert E_1 \vert =4\vert E_2 \vert$.
Do we need to compute the value of $E_1$ and $E_2$ explicitly or is there any other quick way to see this?

$E_1$ and $E_2$ are linear functionals on the space of polynomials of degree at most $2$. So it is enough to prove that $\vert E_1 \vert =4\vert E_2 \vert$ for $f=1,x,x^2$.
