Compute the coefficients

Question

I came upon an exercise which I can not find the solution. I am asked to find the coeffients $a_0$,$a_1$,$b_0$,$b_1$,with the method of undefined coefficients of the following expression
$\int_{x_0}^{x_1}f(x)dx = h({a_0}{f_0}+{a_1}{f_1})+{h^2}({b_0}{f'_0} + {b_1}{f'_1})$
where ${f'_i} = {f'(x_i)} $ and $x_i = x_0 + ih $.

I tried to look into bibliography and all I have found is
$\int_{x_0}^{x_1}f(x)dx = h/2[{f_0} + {f_1]} $
but I am not sure how to use this when no $f'$ is in the proof. Also does $f$ have to be polynomial. Because I think that's missing from the exercise and is a key to my proof.