$f(x)= \begin{cases}\int\limits_{0}^{x}(5-|t-3|) d t, & x>4 \\ x^{2}+b x & , x \leq 4\end{cases}$
where $\mathrm{b} \in \mathbb{R}$. If $f$ is continuous at $x=4$, then which of the following statements is NOT true?
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and More.