Let f(x) be a polynomial of degree 4 satisfying (∫A(t)B(t)dt for t∈[1, x])(∫C(t)D(t)dt for t∈[1, x]) - (∫A(t)C(t)dt for t∈[1, x])(∫B(t)D(t)dt for t∈[1, x]) = f(x) ∀ x ∈ R
where A(x), B(x), C(x) and D(x) are non-constant continuous and differentiable functions. It is given that the leading coefficient (coefficient of x4) of f(x) is 1.
The area included between y = f(x) and y + 2 = 0 between the ordinates x = 0 and x = 3 is
(A) 3/5 sq. units
(B) 33/5 sq. units
(C) 23/10 sq. units
(D) 63/5 sq. units
