If `(x)` is of the form `f(x)=a+b x+c x^2,` show that `int_0^1f(x)dx=1/6{f(0)+4f(1/2)+f(1)}`

Explanation

To show that

\[ \int_0^1 f(x) \, dx = \frac{1}{6} \left( f(0) + 4f\left(\frac{1}{2}\right) + f(1) \right) \]

for a function of the form \( f(x) = a + bx + cx^2 \), we will follow these steps:

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