If $$f(x) = a + bx + cx^{2},$$​ then $$\int_{0}^{1} f(x)\,dx$$​ is:

Correct option is C

Given:
​$$f(x) = a + bx + cx^{2}$$​​
Formula used:
Simpson’s rule (exact for polynomials up to degree 2):
​$$\int_{0}^{1} f(x)\,dx= \frac{1}{6}\left[ f(0) + 4f\!\left(\frac{1}{2}\right) + f(1) \right]$$​​
Solution:
Since f(x) is a quadratic polynomial, Simpson’s rule gives the exact value
of the definite integral on [0, 1].
Hence,
​$$\int_{0}^{1} f(x)\,dx= \frac{1}{6}\left[ f(0) + 4f\!\left(\frac{1}{2}\right) + f(1) \right]$$​​
The correct answer is (c).