Chapter 5, Problem 56RE

Let $F\left(x\right)={\displaystyle {\int }_0^x\frac{t^2-3}{t^4+7}dt}$ .

(a) Find the intervals on which $F$ in increasing and those on which $F$ is decreasing.

(b) Find the open intervals on which $F$ is concave up and those on which $F$ is concave down.

(c) Find the $x\text{-values}$ , if any, at which the function $F$ has absolute extrema.

(d) Use a CAS to graph $F$ , and confirm that the results in parts (a), (b), and (c) are consistent with the graph.