Find the double integral $\int_{0}^1 \int_{y}^1 e^{x^2} \ dx \ dy $

Note that$$\int_0^1\int_y^1e^{x^2}\,\mathrm dx\,\mathrm dy=\int_0^1\int_0^xe^{x^2}\,\mathrm dy\,\mathrm dx=\int_0^1xe^{x^2}\,\mathrm dx.$$Can you take it from here?