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$\left(\int_0^a x d x\right) \leq(a+4), \quad$ then
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The correct answer is:
$-2 \leq a \leq 4$
$\begin{aligned} & \int_0^a x d x \leq a+4 \Rightarrow \frac{a^2}{2} \leq a+4 \\ & \Rightarrow a^2 \leq 2 a+8 \quad \Rightarrow a^2-2 a-8 \leq 0 \\ & \Rightarrow(a-4)(a+2) \leq 0 \Rightarrow-2 \leq a \leq 4\end{aligned}$
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