In this design project, you will write a program that calculates the $$area under the curve$$ of

a polynomial function. The user provides the polynomial$$s coefficients, and the program

returns the $($approximate$)$ value of the area.

A polynomial is defined by its coefficients. For example,

$()=43+2\mathrm{.}123$

is a polynomial of degree three in the variable $$ with coefficients $[3,0,2\mathrm{.}1,4].$

What is the $$area under the curve$$ of a function?