To find the value of the integral of f(x)=(x^2+x), between the limits 1 and 3, we find the integral

Int[ f(x) dx ], x = 1 to x = 3

=> (x^3/3 + x^2/2), x = 1 to x = 3

=> 3^3/3 + 3^2/2 - 1^3/3 - 1^2/2

=> 9 + 9/2 - 1/3 - 1/2

=> 38/3

**The required value if the definite integral is 38/3**