If you mean integrating 2e^(x^2) from 1 to y, then there is no closed form like topsquark mentioned.
However, if you are integrating 2xe^(x^2) from 1 to y, then use a direct substution. Let u(x) = x^2. Then du = 2x dx. Then u(1) = 1 and u(y) = y^2.
Integrating 2xe^(x^2) from 1 to y is the same as integrating e^u from 1 to y^2.
Thus, the integral is e^u | from 1 to y^2.
Thus, e^(y^2) - e^1.
Thus, e^(y^2) - e.
I would suggest reversing the order of integration. By the bounds of your integral, we have and , which implies .
From these we can determine the new bounds are and . So
This should be able to be evaluated.