[tex]\displaystyle\int_0^1e^{-4x}\,\mathrm dx=-\frac14\int_0^{-4}e^u\,\mathrm du[/tex]
where we let [tex]u=-4x[/tex], so that [tex]-\dfrac{\mathrm du}4=\mathrm dx[/tex].
[tex]\displaystyle-\frac14\int_0^{-4}e^u\,\mathrm du=\frac14\int_{-4}^0e^u\,\mathrm du=\frac14e^u\bigg|_{u=-4}^{u=0}=\frac14\left(e^0-e^{-4}\right)=\frac{1-e^{-4}}4[/tex]
