Grapher 2.1: infinity is not infinity

Dear anyone who can help me with this?
When I enter a integral function:
y=integral_0^5 dx(e^{-x})
into Grapher, it plots a straight horizontal line close to y=1.
As the upper limit going down, the line honestly moves close to y=0.
However, if I enter the upper limit to infinity, something weird happens.
It becomes a line y=0.75
Anyone know what is going on here?
Thanks in advance!
BTW, I also notice something wrong in this integral function:
On the above integration limit, one can type up to 23948.09556723854 and still get a proper line close to y=1. But, if you enter any number greater than 23948.09556723854, the function draw y=0 instead.
Message was edited by: Alvyn
Message was edited by: Alvyn

After some email conversation with Yves, he has got me answers that I am not fully satisfied but convinced. I have to thank Yves for the answer to this thread. Thanks to baltwo for redirecting me to Yves too.
The answer is basically on the algorithm Grapher uses for the integration. I one goes to the preferences, he/she will find the "Integration" section in the "Advanced" section where the settings do all the fine tuning. The default method for integration is Romberg and it is likely the best.
As it is numerical integration, error cannot be avoided when the condition goes to extremes.
That's it.

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