Forward Price Evolution

Does anyone know of an example that explains how if future spot rates are lower (higher) than implied by the forward curve, the forward price will increase (decrease)? Why would a trader, who expects lower future spot rates, will go long the forward contract to profit?

If the future spot rates are lower, that implies higher bond price and hence the trader would buy in order to profit

Is it b/c the future spot rates are lower that the present value of the bond was discounted at a lower rate (as compared to the forward rates) that the bond is now priced higher than it was supposed to be?

Yes