Numerical integration of multidimensional integral

I’m looking for software that allows one to numerically integrate multidimensional integrals, hopefully compatible or written in C. I’ve found an answer for one dimensional integrals here: https://stackoverflow.com/questions/1564543/c-math-library-with-integration

Any suggestion or pointer? That hopefully supports parametric bounds, i.e., bounds that not necessarily are number but can also be expressions with the other integration variables involved. For example, for a two dimensional integral in x and y, the lower bound for the integration on y may be 1 – x. My goal is to integrate probability density functions but with domain involving expression as shown above.