If $\int_{-\infty}^{\infty}f(x)\ \mathrm dx=100$ then $\int_{-\infty}^{\infty}f(100x+9)\ \mathrm dx =?$ 
Given $\displaystyle\int_{-\infty}^{\infty}f(x)\ dx=100$, evaluate $\displaystyle\int_{-\infty}^{\infty}f(100x+9)\ dx.$

Question is as above. I'm not sure how to even start. Is the answer $100$? Seems like if the function is bounded from negative infinity to infinity, any transformation just changes the shape. Not sure how to explain this properly though.

Hint: Consider a particular example.  What if $f(x) = 1$ for $0 < x < 100$ and $f(x) = 0$ elsewhere?  What is $f(100x+9)$ in this case?  What is the value of the second integral?
