Example 2: Suppose we have the function F(x) = sin t dt. Let’s evaluate this as x increases from 0 to
π. Obviously F(0) = 0 because there is no area under the curve. So, first, let’s find F . Graphically, we
are looking for the area under the curve y = sin t from t = 0 to t = . It looks like the following:
If we evaluate the integral, we get
F( ) = sin t dt = (−cos t) = −cos + cos 0 = 1 − ≈ 0.134
Now let’s find F( ). It looks like the following: