What is the Formal Definition of the Definite Integral of the function $y = f (x)$ $y=f(x)$ over the interval $[a, b]$ $[a,b]$ ?

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Answer 1 · 2014-09-08T18:48:16

$int_a^bf(x)dx=lim_{n to infty}sum_{i=1}^n f(a+iDelta x)Deltax$ ,
where $Delta x ={b-a}/n$

What is the Formal Definition of the Definite Integral of the function y=f(x)y=f(x)y=f(x) over the interval [a,b][a,b][a,b] ?