Matplotlib animation in Jupyter notebook creates additional empty plot

This has nothing to do with an animation.

The lines

%matplotlib inline
import matplotlib.pyplot as plt
fig, ax = plt.subplots()

will create an output with an empty figure.

You may prevent the output of a cell in jupyter notebook using %%capture.

Cell1:

%%capture
%matplotlib inline
import matplotlib.pyplot as plt
import matplotlib.animation
plt.rcParams["animation.html"] = "jshtml"
import numpy as np

t = np.linspace(0,2*np.pi)
x = np.sin(t)

fig, ax = plt.subplots()
h = ax.axis([0,2*np.pi,-1,1])
l, = ax.plot([],[])

def animate(i):
    l.set_data(t[:i], x[:i])

ani = matplotlib.animation.FuncAnimation(fig, animate, frames=len(t))

Cell2:

ani

You can add plt.close() before the last line.

%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt

from matplotlib import animation
from IPython.display import HTML

plt.rcParams['figure.figsize'] = (5,3)
plt.rcParams['figure.dpi'] = 100
plt.rcParams['savefig.dpi'] = 100
plt.rcParams["animation.html"] = "jshtml"  # for matplotlib 2.1 and above, uses JavaScript
#plt.rcParams["animation.html"] = "html5" # for matplotlib 2.0 and below, converts to x264 using ffmpeg video codec
t = np.linspace(0,2*np.pi)
x = np.sin(t)

fig, ax = plt.subplots()
ax.axis([0,2*np.pi,-1,1])
l, = ax.plot([],[])

def animate(i):
    l.set_data(t[:i], x[:i])

ani = animation.FuncAnimation(fig, animate, frames=len(t))
plt.close()
ani