$1-$ An integral is given below:

${\displaystyle \underset{0}{\overset{0\mathrm{.}8}{}}}(0,2+25x-200x^2+675x^3-900x^4+400x^5)dx$

Write a Python program to calculate the following ones:

a$-$ Find out the analytical solution, $(5$p$)$

b$-$ Solve the integral by "Trapezoidal Rule" taking the step interval: $h=0,1$ and calculate the

percentage error compared to the analytical solution, $(10$p$)$

c$-$ Solve the integral by "Gauss $-$ Legendre $3$ Point Rule" and calculate the percentage error

compared to the analytical solution. $(10$p$)$