Integrate : $\int \large\frac{x^5+1}{x^2+1}$$dx$

Question

$$\begin {array} {1 1} (a)\;\frac{x^4}{4}-\frac{x^2}{2}+\frac{1}{2} \log (x^2+1)+\tan ^{-1} (x^2+1) +c \\ (b)\;\frac{x^4}{4}+\frac{x^2}{2}+\frac{1}{2} \log (x^2+1)+\tan ^{-1} (x^2-1) +c \\ (c)\;x^2+x+c \\ (d)\;None \end {array}$$