My ignorant intuition is since it's the area between sin(x)/x and the x axis, but as you get further into infinity the 1/x still keeps getting smaller slowly bu

My ignorant intuition is since it's the area between sin(x)/x and the x axis, but as you get further into infinity the 1/x still keeps getting smaller slowly but sin(x) always is the same magnitude, the integral gets slightly further away the closer you get to infinity and that slight difference adds up?