# How do I plot a definite integral on Mathematica?

I am not sure how to put this in good format, but I want to plot this on Mathematica:

$$u(t) = \frac{1}{4\pi t} \int\mathrm dy\ \mathrm e^{-y^2/(4t)}\ y\ (1 - y^2)$$

on the interval $$[a, b]$$ where $$a = 0$$ and $$b = 1$$ are the upper and lower bounds.

The integral given in the question can be done symbolically.

Clear["Global*"]

u[t_] = Integrate[1/(4*Pi*t)*E^(-y^2/(4*t))*y (1 - y^2), {y, 0, 1}] //
FullSimplify

(* (1 + 4 (-1 + E^(-(1/4)/t)) t)/(2 π) *)


EDIT: As suggested by Artes

Limit[u[t], t -> 0, Direction -> #] & /@
{"FromAbove", "FromBelow"}

(* {1/(2 π), -∞} *)

Plot[u[t], {t, -5, 5}, PlotRange -> {-0.06, 0.175}]
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