$\text{ Which of the following statements is correct for the function }g\left(\alpha \right)\text{ for }\alpha \in R\text{ such that }$$g\left(\alpha \right)=\underset{\frac{\pi }{6}}{\overset{\frac{\pi }{3}}{\int }}\frac{{\sin }^{\alpha }x}{{\cos }^{\alpha }x+{\sin }^{\alpha }x}dx$

$g\left(x\right)=\frac{1}{2}\left(\frac{\pi }{3}-\frac{\pi }{6}\right)=\frac{\pi }{12}\text{ is a constant function, it is an even function, }$$Hence, it is neither increa\sin g nor decrea\sin g function and it has no inflection points$