This paper shows temperature and acceleration effects on Micro-Electro-Mechanical-Systems (MEMS) gyroscope and a practical solution is presented to mitigate effect of these errors using different methods (Polynomial Curve fitting and Neural Networks). Compensation is performed on the output bias drift data acquired from different MEMS gyroscopes. Performance of compensation techniques is also presented in this study. This paper presents novelty of integrated compensation for both factors (temperature and acceleration) based on empirical data. The compensation is applied on data acquired from ADIS16488, ADXRS450, and XSENS MTi-10 (commercial sensors from Analog Devices and XSENS). 20% improvement in the bias instability is achieved after temperature compensation in ADXRS450 and 50% improvement in XSENS MTi-10 sensors' data. The compensation techniques significantly reduce the rate random walk. The integration time can be increased 4 times for ADIS16488 and ADXRS450 sensors and 8 times for XSENS MTi-10 sensor. The offset present in MEMS gyroscope can also be reduced from 0.05 degrees/sec to 0.001 degrees/sec (50 times improvement) using integrated compensation as compared to 10 times improvement seen by conventional compensation (temperature only) in the XSENS sensor data.