The upper limit is always the larger value (i.e., more positive or less negative. For the limits on the y integration, ##-e^x < -1##, so -1 is the less negative value, and you are correct to put it at the upper limit of integration.
Also, in the future, if you post an image, please take care to post it in the correct orientation. A lot of members here don't like to have to crane their heads 90° to be able to read an image.
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