Integration? No no its ...

Calculus Level 4

\[\int_{1}^{x}A(x)B(x)dx*\int_{1}^{x}C(x)D(x)dx-\int_{1}^{x}A(x)C(x)dx*\int_{1}^{x}B(x)D(x)dx=f(x)\]

If f(x) is a nth degree polynomial and satisfies above equation for all real x, then area bounded by f(x) and the line y=x-1 can be represented as

\[\tfrac{a}{b*c}\]

Find the value of a-b+c

Assumptions:

n is an even natural number.

a,b may not be numbers.

c is a number.

A, B, C, D are non constant continuous functions of x.

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