What is this form of integral equation called and what are the classes of solutions?

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This is probably a quick one for someone familiar with integral equations:

I have an equation of the form $\int_{a}^{b}du \, g(u,v) \, f(u)=c$ with $a$, $b$, and $c$ constant; and $f(u)$ a known function (with $g(u,v)$ unknown).

Since this is a simple form it seems that someone at some point probably studied it extensively, but I can't find any info on it by searching because I don't know what it would be called. It looks like the "reverse" case, with the unknown function being of a single variable and the known being of two, is fairly well known (Fredholm equation).

Many thanks!