What is the integral of ##xe^x## from -infinity to 0?

I found: ##int_(-oo)^0xe^xdx=-1##

I would solve it by parts:
##intxe^xdx=xe^x-int1*e^xdx=xe^x-e^x=##
using your extrema:
##=e^x(x-1)|_-oo^0####=##
##=-1-0=-1##
[where I used the fact that: ##e^0=1 and e^-oo=1/e^oo=0##]

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