Need help with signal conditioning
You don't need an integrator (unless you want to integrate).

when Vin = 0.6, Vout = 9V and Vin = 2.4, Vout = 1V

So it needs to invert (output goes down when input goes up).

(source)
Gain should be : (9-1)/(2.4-0.6) = 4.44 so that gives you the ratio of R2/R1.
In the inverting amplifier, the &quot;+&quot; input is usually connected to 0V but it doesn't have to. It you set it to a voltage V, then :
\$ V_{out}-V = R_2/R_1 (V_{in}-V) \$
Just solve it and you get the voltage you need to put on the &quot;+&quot; input, you can make it with a voltage divider from the supply voltage if its accuracy is good enough, and filter by a capacitor.