Equations on Integration!

Calculus Level 5

\[\large{\int_0^x t \cdot f(x-t)\ \mathrm{d}t = \int_0^x f(t)\ \mathrm{d}t + \sin(x) + \cos(x) -x-1}\]

Find a continuous function \(f(x)\) such that for all real \(x\), the above equation is satisfied. Determine the value of \(f \left( \dfrac{\pi}6 \right)\) to three decimal places.

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