If for a real number $$y$$, $$\left[ y \right]$$ is the greatest integer less than or
equal to $$y$$, then the value of the integral $$\int\limits_{\pi /2}^{3\pi /2} {\left[ {2\sin x} \right]dx} $$ is

Let $$f\left( x \right) = x - \left[ x \right],$$ for every real number $$x$$, where $$\left[ x \right]$$ is the integral part of $$x$$. Then $$\int_{ - 1}^1 {f\left( x \right)\,dx} $$ is

If $$\int_0^x {f\left( t \right)dt = x + \int_x^1 {t\,\,f\left( t \right)\,\,dt,} } $$ then the value of $$f(1)$$ is

The value of $$\int\limits_\pi ^{2\pi } {\left[ {2\,\sin x} \right]\,dx} $$ where [ . ] represents the greatest integer function is