Why a definite integral is not infinite If i consider a definite integral of $f(x)=1$ from $[-1,1]$ in $\mathbb{R}$, why the integral is equal to $2$ even if from $-1$ to $1$ there are infinite points ?
Thanks

Because the definite integral is calculating the area between the curve and the horizontal axis. It isn't just counting points.
In the case of $f(x)=1$ on $[-1,1]$, the region under the curve is a rectangle with length $2$ and height $1$. This gives an area of $2$.
