Write the Integral with the Order of Integration Reversed (Changing $$\int _ { - 1 } ^ { 1 } \int _ { 0 } ^ { \sqrt { 1 + y } } f ( x , y ) \mathrm { d } x \mathrm {~d} y$$

Write the integral with the order of integration reversed (changing the limits of integration as necessary) . $$\int _ { - 1 } ^ { 1 } \int _ { 0 } ^ { \sqrt { 1 + y } } f ( x , y ) \mathrm { d } x \mathrm {~d} y$$

A) $\int _ { 0 } ^ { \sqrt { 2 } } \int _ { \sqrt { x } - 1 } ^ { 1 } f ( x , y ) \mathrm { d } y \mathrm {~d} x$
B) $\int _ { 0 } ^ { \sqrt { 2 } } \int _ { x ^ { 2 } - 1 } ^ { 1 } f ( x , y ) \mathrm { d } y \mathrm {~d} x$
C) $\int _ { 0 } ^ { 1 } \int _ { 1 } ^ { x ^ { 2 } - 1 } f ( x , y ) \mathrm { d } y \mathrm {~d} x$
D) $\int _ { - 1 } ^ { 0 } \int _ { x ^ { 2 } - 1 } ^ { 1 } f ( x , y ) \mathrm { d } y \mathrm {~d} x$
E) $\int _ { 0 } ^ { \sqrt { 2 } } \int _ { \sqrt { x - 1 } } ^ { 1 } f ( x , y ) \mathrm { d } y \mathrm {~d} x$

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