If [x] is the greatest integer $\le$ x, then ${\pi ^2}\int\limits_0^2 {\left( {\sin {{\pi x} \over 2}} \right)(x - [x]} {)^{[x]}}dx$ is equal to :

Question

If [x] is the greatest integer $\le$ x, then

${\pi ^2}\int\limits_0^2 {\left( {\sin {{\pi x} \over 2}} \right)(x - [x]} {)^{[x]}}dx$ is equal to :

2($\pi$ $-$ 1)