Is equal to (where and denotes greatest integer function and signum function respectively)

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

I=\int \left(\log_2\left(\left(\frac{\sin([x]\pi)}{x^2+x+1}\right)+\operatorname{sgn}(x^2+x+1)+1\right)\right)\,dx

is equal to (where

[\cdot]

and

\operatorname{sgn}(\cdot)

denotes greatest integer function and signum function respectively) (a)

x+C

(b)

\cos x+x+C

(c)

\sin x+\operatorname{sgn}(x^2+x+1)+x+C

(d)

-x+C