Evaluate the definite integral:

Given:

First solve for I1:

As we can see that (x-1)≥0 when 1≤x≤4

Now solve for I2:

As we can see that (x-2)≤0 when 1≤x≤2 and (x-2)≥0 when 2≤x≤4

Now solve for I3:

As we can see that (x-3)≤0 when 1≤x≤3 and (x-3)≥0 when 3≤x≤4

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