Suppose we define integral using the following formula `int_(a)^(b)f(x)dx = (b-a)/(2) (f(a)+f(b))`, for more accurate result for `c in (a, b), F(c) = (c-a)/(2) (f(a)+f(c)) + (b-c)/(2)(f(b) + f(c))`.
When `c = (a+b)/(2)`, then `int_(a)^(b) f(x)dx = (b-a)/(4)(f(a) + f(b) + 2f(c))`.
`lim_(trarra)(int_(a)^(t)f(x) dx -((t-a))/(2)(f(t)+f(a)))/((t-a)^(3))=0 forall a` Then the degree of `f(x) ` can at most be

Options

A. `pi//4`
B. `pi(sqrt(2)+1)//4`
C. `pi(sqrt(2)+1)//8`
D. `(pi)/(8)`

Answer

C