No one was able to solve it previously

Calculus Level 4

If \(f(x)=x^{3}-\frac{3}{2}x^{2}+x+\frac{1}{4}\)

Find \(\displaystyle {\int^{\frac{3}{4}}_{\frac{1}{4}} f(f(x)) \text{ d}x}\)

This problem is part of my set Some JEE problems

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