I was watching this video, which shows the following result:
$$\int_0^{100}{e^{\{x\}}}dx=100(e-1)$$
I thought to check the result on Desmos, but it's giving me a different answer! *Note: I am using $\{x\}=x-\lfloor{x}\rfloor$ as the fractional part of $x$.
Typing the integral directly on Desmos gives $\approx167.93$. I have tried typing in the following into Desmos, which is how the result is done by hand:
$$\sum_{n=1}^{100}\int_{n-1}^ne^{x-n+1}dx$$ and Desmos actually gives the correct answer here, $100(e-1)$.
Is there something that I'm missing or typing incorrectly into Desmos, or is it just wrong?
As a reference, here is what I am getting from Desmos. _____________________________________________________
Update: As I was typing the question, I thought to input $\int_0^{k}{e^{\{x\}}}dx$ and $k(e-1)$ into Desmos, and I noticed that the values to start to drift from eachother at around $k=30$. This still doesn't tell me what the issue is though.
Just note that
$$ \int_{0}^m e^{\{x\}}\,d x=\sum_{k=0}^{m-1}\int_{k}^{k+1}e^{\{x\}}\,d x=\sum_{k=0}^{m-1}\int_{0}^1 e^{x}\,d x=\sum_{k=0}^{m-1}(e-1)=m(e-1) $$
for any $m \in \mathbb{N}$. Now just compute in a calculator for $m=100$ and you get $100(e-1)\approx 171,8$ so there is something wrong with the computation of $\int_{0}^{100}e^{\{x\}}\,d x$ by Desmos.