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##]