The function f(x), that satisfies the condition $f(x) = x + \int\limits_0^{\pi /2} {\sin x.\cos y\,f(y)\,dy} $, is :

Question

The function f(x), that satisfies the condition
$f(x) = x + \int\limits_0^{\pi /2} {\sin x.\cos y\,f(y)\,dy} $, is :

$x + {2 \over 3}(\pi - 2)\sin x$

$x + (\pi + 2)\sin x$

$x + {\pi \over 2}\sin x$

$x + (\pi - 2)\sin x$

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