Integral equations of the first kind are a typical example of ill-posed problems \cite{Groetch,groetsch,Kress}. Referring to the univariate case, they take the form \begin{equation*} \int_{a}^b k(x,y) f(x) dx =g(y), \qquad y \in [c,d], \end{equation*} where $k$ is a given kernel, $g$ is a known right-hand side, and $f$ is the unknown solution. In this talk, we propose a procedure to compute the minimal norm solution of the given equation. \begin{thebibliography}{99} \bibitem{Groetch} Groetsch, C.~W. Integral equations of the first kind, inverse problems and regularization: a crash course. In {\em Journal of Physics: Conference Series} (2007) 73: 012001. \bibitem{groetsch} Groetsch, C.~W. {Elements of applicable functional analysis}, volume~55. M. Dekker, 1980. \bibitem{Kress} Kress, R. Linear Integral Equations, Springer, Berlin, 1989. \end{thebibliography}