Math Mystery

It is amazing how easily you can get things wrong when you forget the basics. Here is a case and point from today, I was recalling the Taylor series of e^x, and something didn't add up. First lets look at the intergral of e^x:



Noting the Taylor Series of e^x:





Clearly these two methods yield a different result. Spot the error that I made, it took me a second to figure it out....