Let a function f: R → R be defined as: f(x)= {∫_0^x(5-|t-3|) d t, x>4; x^2+b x, x ≤ 4} where b ∈ R. If f is continuous at x=4, then which of the…

Let a function $\displaystyle f: \mathbb{R} \rightarrow \mathbb{R}$ be defined as : $$f(x)= \begin{cases}\int_0^x(5-|t-3|) d t & , x>4 \\ x^2+b x & , x \leq 4\end{cases} $$ where $\displaystyle \mathrm{b} \in \mathbb{R}$. If $\displaystyle f$ is continuous at $\displaystyle x=4$, then which of the following statements is NOT true?