$$\int_{0}^{10\pi}(\lfloor arcsecx \rfloor+\lfloor arccotx \rfloor)dx$$
I have tried disintegrating the trigonometric functions into their acceptable principle domains, and then further disintegrate the integral into more parts opening up the greatest integer function, however I have failed miserably.
One thing I clearly do not understand is, how can $arcsec(x)$ even exist under $(0,1)$. Please shed some light.