Evaluate the integral
Split the limits of integration into two or more intervals on each of which the integrand has the same sign, so that, on each interval, you can replace || by either +() or -()
Since the quantity inside the absolute value sign is a product of linear terms, x(x-5)(x+7), it is easy to see that it is 0 exactly at x= -7, x= 0, and x= 5. Break the integral into two parts, from -7 to 0 and from 0 to 5, do those integrals separately (being careful about the sign) and add the results.
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