`text(Fundamental theorem of integral calculus)`

`int_a^b f(x)dx=Lim_( underset (n->oo) (h to 0 )) h [f(a)+f(a+h)+f(a+2h)+.....+f(a+(n-1)h)]`

or `int_a^b f(x) dx=Lim_( underset (n->oo) (h to 0 )) h sum_(r=0)^(n-1)f(a+rh)` where `b-a=nh`

`text(Note:)` Evaluating a definite integral by evaluating the limit of a sum is called evaluating definite integral by first
principle or by a b initio method.

Put `a=0` & `b=1` `=>nh=1` we have

`int_0^1 f(x) dx= 1/n sum_(r=0)^(n-1) f(r/n) ; ` replace `1/n to dx ; sum to int ; r/n to x`