$[$FTC$5*]($Section $5\mathrm{.}3$ part $1)$ Shown below is the graph of a function $f(x).$ What is the value of ${\displaystyle \underset{2}{\overset{5}{}}}{f}^{\text{'}}(x)dx?$

$[$FTC$8]($Sections $5\mathrm{.}5$ and $5\mathrm{.}6)$ Substitution Rule. Evaluate the integral by using an appropriate substitution.

a$.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}x(1-x{)}^{99}dx$

b$.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{10x}{x^2+6}dx$

c$.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}y\sqrt[\phantom{2}]{y^2+10}dy$

d$.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{sin(\sqrt[\phantom{2}]{x})}{\sqrt[\phantom{2}]{x}}dx$

e$.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{e}^{sin()}cos()d$

f$.{\displaystyle \underset{0}{\overset{4}{}}}\sqrt[\phantom{2}]{2x+1}dx$

g$.{\displaystyle \underset{0}{\overset{\frac{}{4}}{}}}se{c}^2()tan()d$

h$.{\displaystyle \underset{0}{\overset{\sqrt[\phantom{2}]{}}{}}}co{s}^2(2)sin(2)d$