F(x) for x --> + infinity = 0
F(x) for x --> - infinity = 0
F(x) for x --> 0+ = 1 (Proof for this is too extensive for me to cover it at this time of night, however, it should be in your textbooks?)
F(x) for x --> 0- = 1
As x is close to infinity the absolute value of sin(infinity) is insignificant. However, the real value of sin(infinity) will change between -1 < x < 1. Hence, the function will 'go up and down' the x axis, going closer and closer to 0, for incredibly high or low values of x.
Edit: If you're in for more of a challenge, try sketching sin (1/x) for infinitesmal values of x!