The function $f$ is continuous and differentiable. A portion of the graph of $f^{\text{'}}$ is given above. Let $f(0)=-3.$

a$)$ Find the intervals on which $f$ is both decreasing and concave down. Justify.

b$)$ Let $p(x)=e^{-f(x)}.$ Is the right Riemann sum approximation of ${\displaystyle \underset{2}{\overset{6}{}}}p(x)dx$ an overestimate or an underestimate? Give a reason.

c$)$ Write an integral expression to find the arc length of $f$ over $-2,1.$

d$)$ Let $g(x)$ be a twice differentiable function defined by $g(x)=2x+3-{\displaystyle \underset{1}{\overset{e^{2x}}{}}}{f}^{\text{'}}(t-1)dt.$ Find the second$-$degree Maclaurin polynomial for $g(x).$