\[ \large \int_0^1 x^2 \cos x \sin x \, dx \]

If the integral above is in the form of

\[ \dfrac {-A + B\sin C - D\cos C}E , \]

where \(A,B,C,D\) and \(E\) are positive integers, find the minimum value of \(A+B+C+D+E\).

**Clarification**: Angles are measured in radians.

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