$(1)$ Let $A(x)$ be the accumulation function defined by

$A(x)={\displaystyle \underset{1}{\overset{x}{}}}t{e}^{(t^3)}dt$

$($a$)$ Use the first fundamental theorem of Calculus to compute $A^{\text{'}}(x).$ Then find the intervals in which $A(x)$ is increasing or decreasing.

$($b$)$ Find $A^{\text{'}\text{'}}(x)$ and the intervals in which $A$ is concave up and concave down.