just need to verify this.

if a have a function f(x) and a function g(x) and the area under f(x)

from a known a to a variable x is (integral from a to x of)f(x);

let f1(x)= (integral from a to x of)f(x);

and

the area under g(x) from the same variable x to a known b is

(integral from x to b of)g(x)

let g1(x)=(integral from x to b of)g(x);

now let c(x)= f1(x)+g1(x);

first isnt c the area of the two regions

and isnt

c'(x)(the derivative of c) the function of the curve above the two

regions(i.e region under f1(x) and region under g1(x))

between a and b?

Or at least if the function of the curve above the two

regions(i.e region under f1(x) and region under g1(x))

is fn(x)

isnt fn(b)=c'(b);

by second fundamental theorem of calculus

would be greatful for any reply.thanks