Consider the following change in integration limits$.$

${\displaystyle \underset{x=a}{\overset{b}{}}}f(x)dx={\displaystyle \underset{t=-1}{\overset{1}{}}}g(t)dt$

where $a=-4,b=5,$ and $f(x)=x^6+2(-x{)}^3+12\mathrm{.}2.$

a$)$ Make use of the necessary lines below to construct a python code that will define the function $g(t).$

b$)$

Assuming, that you have defined the function, $g(t),$ make use of the necessary lines below to construct a program to obtain the integral value by using a three point Gauss$-$Quadrature rule.

$a,b=-4,5$

return $x^{*****6}+2+(-x)****3+12*2$

for $i$ in range $($ len$($c$))$:

$x=\frac{b-a}{2}***t+\frac{a+b}{2}$

return $\frac{b-a}{2}**f(t)$

defg$(t,a,b)$ :

deff$(x)$ :

print $($I$)$

$I=I+c[i]**g(x[i],a,b)$

c$,x=[\frac{5}{9},\frac{8}{9},\frac{5}{9}],[0\mathrm{.}7740,0,-0\mathrm{.}7746]$

$I=0$