gyroscope to orientation

good evening guys ;D!

to start off, integration of gyroscope output which is angular rate gives us angle right?

right now im really stuck as to what is the maximum angle/orientation that you can derive from gyroscope data.
im using an adxrs300 gyroscope which has the following data

maximum range = +/- 300 (deg/second)
bandwidth / sampling rate = 50 hz

to get the maximum angle we multiply this to the (1/bandwidth of the gyroscope) right? so we get 300 / 50 = 6 degrees. does this mean that the maximum detectable angle is 6 degrees?

You need to pay more attention to the dimensions of your units.
Six degrees is the maximum change you can register in one sample period, but you can have lots of sample periods.

can you please share some tips or at least point me in the right direction on how to actually perform "integration" of the gyroscope's rate? what ive done so far is something like (which i now realize is wrong)

Angle = DegPerSecGy * (1/50); //gyroscope sampling rate

i do this for ALL gyroscope data i have. the result is that the even though i tilt and tilt my gyroscope the values always fall near zero. thank you!

Integration at its simplest is just addition for a period of time.
So, if you read a turn rate of 5 degrees per second for 50 samples at 50Hz, then you've turned through 5 * 50 degrees.

so suppose every time step i have a gyroscope output which i will scale to DegPerSecGy, then the angle would then be
Angle += DegPerSecGy * (1/50) ?

i do not need to average it or divide it by anything?