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If for all real triplets $(a, b, c)$, $f(x) = a + bx + cx^2$; then $\int_0^1 f(x),dx$ is equal to:
(1) $2\left{3f(1) + 2f\left(\dfrac{1}{2}\right)\right}$
(2) $\dfrac{1}{2}\left{f(1) + 3f\left(\dfrac{1}{2}\right)\right}$
(3) $\dfrac{1}{3}\left{f(0) + f\left(\dfrac{1}{2}\right)\right}$
(4) $\dfrac{1}{6}\left{f(0) + f(1) + 4f\left(\dfrac{1}{2}\right)\right}$
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