the question is

Let F(a) be the function which gives the area under the graph of y=x*e^-x between x=0 and x=a for a>0

i found F(a) to be (-x*e^-x)-(e^-x)

then evaluated with the given endpoints i got

(-a*e^-a)-e^a+1

(not sure if this is correct)

the second question is

is F increasing or a decreasing function?

is it the same that if the second derivative tells the concavity? pointers anyone?