JEE Math Practice Question

If for all real triplets (a, b, c), ƒ(x) = a + bx + cx2; then $$\int\limits_0^1 {f(x)dx} $$ is equal to :

1. A.$${1 \over 6}\left\{ {f(0) + f(1) + 4f\left( {{1 \over 2}} \right)} \right\}$$
2. B.$$2\left\{ 3{f(1) + 2f\left( {{1 \over 2}} \right)} \right\}$$
3. C.$${1 \over 3}\left\{ {f(0) + f\left( {{1 \over 2}} \right)} \right\}$$
4. D.$${1 \over 2}\left\{ {f(1) + 3f\left( {{1 \over 2}} \right)} \right\}$$