Compute the spectrum of the integral operator $K:L^2([0,1]) \to L^2([0,1])$ defined as $(Kx)(t) = \int_0^t x(s) ds$

Question

Let $K:L^2([0,1])\rightarrow L^2([0,1])$ be the linear operator defined by $$(Kx)(t)=\int_0^tx(s)ds, \quad x \in L^2([0,1]).$$

Now I have to compute the spectrum, but I don't have any idea how to do this.

If I would know when $(K-\lambda)$ is bijective then I would be finish.

Does there exists any "trick" for this kind of problem? (spectrum of integral operators)