Fix $p\in [1,+\infty)$ and let $f\in L_p[0,T]$. show that the expression $$f_n(t)=\int ^t_0 ne^{n(s-t)}f(s) ds\quad t\in[0,T], n\in \mathbb{N}$$ defines a sequence of continuous functions such that $\lim_{n\to \infty} \|f_n-f\|_{L^p}=0$.
$$\lim_{n\to \infty} \|f_n-f\|_{L^p}=\lim_{n\to \infty} \|\int ^t_0 ne^{n(s-t)}f(s) ds-f\|_{L^p}$$
I think if we write $f$ in terms of integral we can do processed but im not getting any idea. Any help please