Name for problem of reconstructing a function from partial derivatives? Reconstructing a single variable function from its derivative is simply called integrating. But say we have an unknown multivariable function $f$ and know its partial derivatives. To illustrate for two variable $f$, Is there a name for the problem of reconstructing $f(x,y)$ from $\partial_xf(x,y)$ and $\partial_yf(x,y)$?
This problem doesnt always have a solution if I'm not mistaken.

It's known as finding a potential of a vector field. The vector field is $(\partial_x f,\partial_y f)$, and $f$ itself is the potential (sometimes also called the potential function).
Like here, for instance: https://mathinsight.org/conservative_vector_field_find_potential.
