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Your sage code can be replaced by:

var('a b')
assume(a>0)
I0=integrate(exp((-a*x^2+b*x)),x,-oo,oo)
var('x_0, x_1, y_0, y_1, d, k, R_0')
I1=I0.subs({a:1/(2*R_0^2) - i*k/(2*d),b:i*k*x_1 / d})
%display latex
I1