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If for all real triplets \((a, b, c), f(x)=a+b x+c x^2\); then \(\int_0^1 f(x) d x\) is equal to [JEE Main 2020, 9 Jan (…

Q1

If for all real triplets \((a, b, c), f(x)=a+b x+c x^2\); then \(\int_0^1 f(x) d x\) is equal to

[JEE Main 2020, 9 Jan (Shift 1)]

a

\(\frac{1}{3}\left\{f(0)+f\left(\frac{1}{2}\right)\right\}\)

b

\(\frac{1}{3}\left\{f(1)+3 f\left(\frac{1}{2}\right)\right\}\)

c

\(\frac{1}{6}\left\{f(0)+f(1)+4 f\left(\frac{1}{2}\right)\right\}\)

d

\(2\left\{3 f(1)+2 f\left(\frac{1}{2}\right)\right\}\)

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