I have been trying to calculate the area under the graph of a PDF (Probability density function) for a normal distribution. The standard form of its PDF is $$\frac{e^{-(x-\mu)^2/2\sigma^2}}{\sqrt{2\pi}\sigma}$$ where $\mu$ is mean and $\sigma$ is standard deviation. The indefinite integral of this is $$\frac{1}{2}\operatorname{erf} \left(\frac{x-\mu}{\sqrt2\sigma}\right)+C$$ where $\operatorname{erf}$ is the error function (https://www.wikiwand.com/en/Error_function) and $C$ is the constant of integration. When I apply the limits from $-\infty$ to $\infty$, Wolfram Alpha is unable to compute it.
How then can I calculate the area under the PDF for the Normal Distribution?