$[3$ marks$]$ Find a function $f$ such that $f^{\text{'}}(x)=x^3$ and the line $x+y=0$ is tangent to the graph of $f.$

$[3$ marks$]$ If $f(x)=\sqrt[\phantom{2}]{x}-2,1x6,$ find the Riemann sum with $n=5$ correct to $3$ decimal places taking the sample points to be the midpoints.