$\int_0^5 {\cos \left( {\pi \left( {x - \left[ {{x \over 2}} \right]} \right)} \right)dx} $, where [t] denotes greatest integer less than or equal to t, is equal to:

Question

$\int_0^5 {\cos \left( {\pi \left( {x - \left[ {{x \over 2}} \right]} \right)} \right)dx} $,

where [t] denotes greatest integer less than or equal to t, is equal to: