Let $f:\mathbb{R}\rightarrow\mathbb{R}$ Lebesgue integrable. Prove $\int{f(x)dx}=\int{f(x+t)}dx$

Question

Let $f:\mathbb{R}\rightarrow\mathbb{R}$ Lebesgue integrable. Prove

$$\int{f(x)dx}=\int{f(x+t)}dx$$

My attempt:
Suppose $f\geq 0$, Let $\varphi$ an increasing sequence $0\leq\varphi_{n}\leq f$ of simple functions such that $\varphi_{n}\uparrow f$ and we have by Monotone Convergence Theorem(Beppo-Levy) that

$$\int f=\lim_{n}\int\varphi_{n}$$

here i'm stuck. can someone help me?