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I want to numerical integrate:

$$\int_{-\infty}^{A_1} \int_{-\infty}^{A_2-x_1} p(x_1)p(x_2)dx_1dx_2 ,$$ where $p(x_i)$ is a random variable that has a normal distribution with mean $\mu_i$ and standard deviation $\sigma_i$.

I faced with several problems:

1. I can't integrate even this simply integral:

import scipy.stats as st

integrate(st.norm.pdf(x), x)

The result is error: TypeError: ufunc 'isnan' not supported for the input types, and the inputs could not be safely coerced to any supported types according to the casting rule ''safe''

1. How to integrate multiple integrals with different $A_i$.