Let $f(x)=x^2$. $df(x)=2xdx$
For $x=0$: $f(0+dx)-f(0)=0$. Thus $f(dx)=0$.
I want to find area under the curve $f(x)=x^2$ from $0$ to $b$: $\int x^2dx = f(0)dx + f(0+dx)dx + f(0+2dx)dx + ... + f(0+(n-1)dx)dx$ where $dx=b/n$, $n=\infty$.
But if $f(0+dx) = 0$ as I mentioned above, then I get wrong sum: $f(0)dx + f(0+dx)dx + ... = 0dx + 0dx + ...$
What is wrong with my reasoning?
Thanks.