Slight mistake with Integral, I can't see why though.

I am having a small problem with this question,

$\displaystyle \int\frac{1}{2}(e^x-e^{-x})dx$

My workings are:

Breaking it down into two terms gives:

$\displaystyle \int(e^{x})dx=\frac{1}{1}e^{1x}+c=e^{x}+c$ and $\displaystyle \int(-e^{-x})dx=\frac{1}{-1}e^{-1x}+c=-e^{-x}+c$

Combining it all together then gives:

$\displaystyle \int\frac{1}{2}(e^x-e^{-x})dx=\frac{1}{2}(e^{x}-e^{-x})+c$

My mistake is inside the brackets, I am getting $\displaystyle -e^{-x}$ when the solution gives $\displaystyle +e^{-x}$

Can anybody see where I am going wrong?

Many thanks.