Why do I get a complex number of this integral?

fun = @(y) y.^-0.5.*exp(-(y-0.01).^2./0.5);
theta = integral(fun,-Inf,Inf)
theta1 = quadgk(fun,-Inf,Inf)

theta =

   1.5388 - 1.5097i

theta1 =

   1.5388 - 1.5097i

Answer 1

[Torsten]

Your function "fun" is complex-valued if y < 0 because of the y^(-0.5) term.

Best wishes

Torsten.

Answer 2

[Walter Roberson]

You have y.^-0.5 as a component of the expression. When y is negative, that is going to be an imaginary value. None of the other components are imaginary so there is nothing to "cancel" the imaginary component.