There are some functions whose antiderivatives cannot be expressed in closed form. You can see this function on the Plot.
Clear["Global`*"]
f[x_] := 1/Sin[x^2];
ep = 1/100;
ff = FunctionInterpolation[f[x], {x, ep, 1.772}, MaxRecursion -> 20];
F = Integrate[ff[x], x];
Plot[{f[x], F - 1/ep}, {x, ep, 1.772}, PlotLegends -> {"f[x]", "\[Integral]f[x]"}]
Series expansion of the integral at x=0:
integralseries = Normal@Integrate[Series[f[x], {x, 0, 50}], x]
(*-(1/x) + x^3/18 + x^7/360 + (31 x^11)/166320 + (127 x^15)/9072000)*)
Plot[{f[x], F - 1/ep, integralseries}, {x, ep, 1.772}, PlotLegends -> {"f[x]", "\[Integral]f[x]", "integralseries"}, PlotStyle -> {Blue, Thin, {Thick, Dashed}}]
