# What is f(x) = int e^x dx if f(0)=-2 ?

${e}^{x} - 3$
We have, $f \left(x\right) = \int {e}^{x} \mathrm{dx}$ which comes out to be ${e}^{x} + C$ where $C$ is the constant of integration.
We also have $f \left(0\right) = - 2$.Plugging in this value in the expression we derived earlier, we get ${e}^{0} + C$=-2 or $C$=-2-1 which is -3. Thus,the expression comes out to be ${e}^{x} - 3$