$$f ( x ) = \begin{cases} 1 , & x \leq 1 \\ x ^ { 2 } + a x + b , & 1 < x < 3 \\ 5 , & x \geq 3 \end{cases}$$
If the function is continuous on the set of real numbers, what is the difference $a - b$?
A) $-4$
B) $-1$
C) 2
D) 3
E) 5
$$f ( x ) = \begin{cases} 1 , & x \leq 1 \\ x ^ { 2 } + a x + b , & 1 < x < 3 \\ 5 , & x \geq 3 \end{cases}$$

If the function is continuous on the set of real numbers, what is the difference $a - b$?

A) $-4$\\
B) $-1$\\
C) 2\\
D) 3\\
E) 5