Difference in way of taking limit of improper integral

Question

So I need to think of an example of a function $f\colon [-1, 1] \to \mathbb R$ such that $$ \lim_{t\to 0}\int_{-1+t}^{1-2t}f(x)\ dx\neq \lim_{t\to 0}\int_{-1+2t}^{1-t}f(x)\ dx. $$ My thought was using a trignometric function to play with the $2t$ part, but it's not quite working. Does any elementary function work here or do I need to play with it piecewise?