I was going through some questions on pointwise and uniform convergence. Got stuck in one of those which says:
Let $g_n(x) = \sin^2(x+\frac{1}{n})$ be defined on $[0,\infty).$
and $f_n(x) = \int_0^xg_n(t)\,dt.$
I am supposed to discuss about its uniform-convergence of $(f_n).$
The terms are really looking complicated to try it by the definition. Should I first show that $(g_n)$ is uniformly convergent? How am I supposed to do even that?
Help, please.