If $\int \large\frac{dx}{x^2+2x+2}$$=f(x) +c,$ then f(x) is equal

Question

$$\begin {array} {1 1} (a)\;\tan^{-1}(x+1) & \quad (b)\;2 \tan^{-1} (x+1) \\ (c)\;-\tan^{-1} (x+1) & \quad (d)\;3 \tan^{-1} (x+1) \end {array}$$