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.