I don't understand what this math problem is asking for can someone help?

Only one integral is needed:

the integral from x = 4 to x = 7 of

(x^2 + 2x - 15) dx.

After integration you have

(1/3)x^3 + x^2 - 15x;

plug in x = 7 and x = 4, you get

(1/3)(343 - 64) + (49 - 16) - 15(7 - 4)

= (1/3)(279) + 33 - 45

= 81.

Do check my arithmetic.

The wording of this question is very odd. If it's asking for the area of the region bounded by

          y = x² + 2x - 15

          x = 4

          x = 7

This can be found by taking one integral:

            ₇                                                    ₇

          ∫  x² + 2x - 15 dx = (⅓ x³ + x² - 15x ⃒

          ⁴                                                      ⁴

                                     = 58.33 - (-22.67)

                                     = 81      ...................ANS

draw it out. from the graph, you want the area under y = x² + 2x - 15 from 3 to 7, one integration.

although that one integral is broken down into 3 using the rule ∫(a+b)du = ∫a du + ∫b du

A = ∫ (x² + 2x - 15) dx   from 3 to 7

A = (1/3)x³ + x² – 15x     from 3 to 7

A = (1/3)7³ + 7² – 15•7  – ((1/3)3³ + 3² – 15•3)

A = 343/3 + 49 – 105  – 9 – 9 + 45

A = 114 1/3 – 29 = 85 1/3

edit: missed the x= 4, but that just changes it a bit to

A = (1/3)x³ + x² – 15x     from 4 to 7

A = (1/3)7³ + 7² – 15•7  – ((1/3)4³ + 4² – 15•4)

A = 343/3 + 49 – 105  – 64/3 – 16 + 60

A = 279/3 – 12 = 81