Finding a nonzero continuous function that satisfies this integral equation, but not unique?

Question

If $h(x)$ is such that it satisfies $$ h(x) = \lambda \int_a^b K(x,y) h(y)\, dy $$ Then for $\phi(x)$ a solution of $$ \phi(x) = f(x) + \lambda \int_a^b K(x,y)\phi(y)\, dy $$ it is true that $\phi + h$ is also a solution. But I am confused as to why this does not violate the uniqueness of solutions to these integral equations?