How the noise in time domain affect the power in frequency domain after FFT?
You have problems in defining the noise and sampling frequency. Your noise is not zero mean and your sampling rate is not well defined. Following simple Python code computes the DFT magnitude of the sine plus noise example. (Note: I'm not a python user so please modify the code as necessary)

# -*- coding: utf-8 -*-

import numpy as np
import matplotlib.pyplot as plt
from scipy.fftpack import fft
import numpy.random as npr


N = 1000                # Set signal sample length

t1 = -5;                # Simulation begins at t1
t2 =  5;                # Simulation  ends  at t2
x = np.linspace(t1,t2,N);# Define the sampling grid as x[n]

Ts = (t2-t1)/N;         # Compute resulting sampling period
Fs = 1/Ts;              # Compute resulting sampling rate

noise = (npr.random(N)-0.5); # Generate ZERO MEAN uniform noise

fsin = 0.2*Fs;            # Sine Wave Frequency in [0:Fs/2]  
y = np.sin(2*np.pi*fsin*x) + noise    # Generate SINE + Noise


# Take FFT and display its MAGNITUDE
w = np.linspace(0,2,N)
waves = fft(y,N)
plt.plot(w,abs(waves))


Where the resulting plot is: