Answer:
Observe that f(x) is a continuous function when [tex]x<1\; and\; x>1[/tex] because is a polynomial. The possible problem may occur in x=1.
Then, f(x) is discontinuous in x=1 if the limits of f to the right and the left of 1 exist and are different or if some of those limits doesn't exist.
Let's calculate the limits:
[tex]lim_{x\rightarrow 1^+}f(x)=lim_{x\rightarrow 1}(x+3)=1+3=4[/tex]
[tex]lim_{x\rightarrow 1^-}f(x)=lim_{x\rightarrow 1^-}(x^2+4)=1^2+4=5[/tex]
Since, [tex]lim_{x\rightarrow 1^-}\neq lim_{x\rightarrow 1^+}[/tex] then f(x) is discontinuous in x=1.
