$$f(x) = \begin{cases} 3 - x, & x < 2 \\ 2x - 3, & x \geq 2 \end{cases}$$
What is the value of the integral $\displaystyle\int_{1}^{3} f(x+1)\, dx$?
A) 2
B) 4
C) 6
D) 8
E) 10
$$f(x) = \begin{cases} 3 - x, & x < 2 \\ 2x - 3, & x \geq 2 \end{cases}$$

What is the value of the integral $\displaystyle\int_{1}^{3} f(x+1)\, dx$?

A) 2\\
B) 4\\
C) 6\\
D) 8\\
E) 10