Exponential Decay Curve

Hello,
I have a task on integration which involved finding the area under and exponential decay curve, I think I have the correct answer however I'm not sure it should be a negative value as it's an area. Can someone please help me clarify?
Question.
Determine the area under the following exponential decay curve between 2 seconds and 4 seconds;
y=∫(e^(-t))dt
My answer
integral is -e^(-t)+C
Now we calculate with time range, omitting the C as it is a constant.
y=∫e^(-t) dt=(-e^(-4))-(-e^(-2))
y=(-e^(-4))-(-e^(-2))
-e^(-4)≈0.0183
-e^(-2)≈0.1353
∴y≈0.0183-0.1353=-0.117
In my mind an area cannot be a negative number, unless in this instance the negative number indicates the area is below the axis? Any help or clarification would be greatly appreciated!