How to plot a single variable function defined by a integral (for example, Gaussian error fucntion, erf(x)) more efficiently?

Dear all,

I want to know how to plot a single variable function defined by a integral more efficiently?

For example, Gaussian error fucntion, .

I know that erf(x) is a build-in function of MATLAB. But I want to know the general way to do this. Currently I am using a for-loop to achieve it. Here is my MATLAB code. Thank you.

clearvars; close all; clc;
f = @(t) (2.0/sqrt(pi))*exp(-t.^2);
x = linspace(-3,3,61);
fval = zeros(1,numel(x));
for i=1:numel(x)
    fval(i) = integral(f,0,x(i),'RelTol',1e-15);
end
hf = figure; plot(x,fval,x,erf(x));