Nonscalar arrays of function handles are not allowed; use cell arrays instead.

clc; 
clear all; 
close all;
X0 = linspace(0.1,0.99,50);
for i = 1:length(X0)
    Ts = 1;
    t(i) = Ts*acos((Ts-X0(i))/Ts);
    v(i) = sqrt(1-((Ts-X0(i))/Ts).^2);
    dE(i) = @(v,t) 0.5*(-((X0(i)-Ts)./Ts).*sin(t(i)./Ts)+v(i).*sin(t(i)./Ts)+Ts).^2;
    E(i) = integral2(dE,0,t(i),0,v(i))
end