The cyber challenges faced by cybercriminals are growing dramatically as the power system strives to become more intelligent and more stable. Load forecasting is a well-known problem in the energy management field, but the state-of-the-art lacks contributions that consider data integrity aspects. Despite the existing effective methods on load forecasting, power system requires robust schemes that are also successful in performing accurate load forecasting under cyber-attacks. A novel cyber-attack named Civil Attack (CA) is employed and faced by the two non-linear regression methods. In recent years, numerous regression techniques such as methods called Multiple Linear Regression (MLR), Artificial Neural Network (ANN), Support Vector Regressor (SVR) and etc., were employed to perform electricity load forecasting under false data injection (FDI) attacks. While all of the techniques listed are inaccurate in zones with high load covariance, mostly industrial zones, we propose two nonlinear methods called Gaussian Process Regression (GPR) with optimized kernel functions and Random Forest Regression (RFR) to address the problem, while the data integrity attack is used for comparing our methods with other proposed methods.