I have the following exponential distribution:
$$f(\lambda, x) = \begin{cases} \lambda e^{-\lambda x} &\text{if } x \geq 0 \\ 0 & \text{if } x<0. \end{cases}$$
I need to show that this expression integrates into
$$F(\lambda, x) = \begin{cases} 1-e^{-\lambda x} &\text{if } x \geq 0 \\ 0 & \text{if } x<0. \end{cases}$$
I know that the integral of a pdf is equal to one but I'm not sure how it plays out when computing for the cdf. I computed the indefinite integral of $\lambda e^{-\lambda x}$ and got $-e^{-\lambda x} + C$