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 the line y = x - 1 and the curve y = f(x) is
(A) 2/5 sq. units
(B) 3/10 sq. units
(C) 7/10 sq. units
(D) 7/5 sq. units