I was trying to get the CDF of the exponential through the pdf. I know that the relationship between the pdf and the cdf is that the pdf is the derivative $ \lambda \exp(-\lambda x) $. But I don't quite understand how the CDF is then $ 1 - \exp(-\lambda x) $.
When I tried to find the cdf I only put it as $\exp(-\lambda x)$. My guess is that this has something to do with the bounds of integration that I'm overlooking. Thank you for any help you can give!