Integration of some floor functions Can anyone please answer the following questions ?
1) $\int\left \lfloor{x}\right \rfloor dx$
2) $\int$ $ \left \lfloor{\sin(x)}\right \rfloor $ $dx$
3) $\int_0^2$ $\left \lfloor{x^2+x-1}\right \rfloor$ $dx$
4) $\int_o^\pi$ $\left \lfloor{x(1+\sin(\pi x)}\right \rfloor$
Also can anyone please make me understand the way in which to proceed in these types of sums?
$\left \lfloor{x}\right \rfloor$ is the floor function
Thanks

$$\lfloor sinx\rfloor $$ is equal to either 0 or 1 or -1, so integrating it should be simple
