How to solve $-\Delta f(x,y) = 1, \ \ (x,y) \in (0,1)^2$, $f(x,y)=1, \ \ (x,y) \in \partial (0,1)^2$

Question

Problem

Solve : $-\Delta f(x,y) = 1, \ \ (x,y) \in (0,1)^2$, $f(x,y)=1, \ \ (x,y) \in \partial (0,1)^2$

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Try

I'm not familiar with the problem, so just spreading the formula out,

$$ - \frac{\partial^2}{\partial x^2} u(x,y) - \frac{\partial^2}{\partial y^2} u(x,y) = 1 $$

but I do not have any ideas on the Ansatz of the solution. Any help?