Definite integral giving negative value as a result? I want to calculate definite integral
$$\int_{-2}^{-1} \frac{1}{x^2}e^{\frac{1}{x}} dx = \Omega$$
$$\int \frac{1}{x^2}e^{\frac{1}{x}} dx=-e^{\frac{1}{x}}+C$$
so:
$$\Omega = [-e^{\frac{1}{-2}}]-[-e^{\frac{1}{-1}}]=-\frac{1}{\sqrt{e}} + \frac{1}{e}$$
which is a negative value. I believe it should be positive.
What went wrong in the process? 

What you effectively did was swap the order of evaluation for the fundamental theorem of calculus. Recall:
$$\int_a^b f(x)dx = F(b) - F(a)$$
when the antiderivative of $f$ is $F$. You instead have $F(a) - F(b)$ ($a=-2,b=-1$) in this case. The end result is merely a sign error - you have precisely the negative of the answer which you should expect.
