Integrity - the bonus damage is added separately based of the (updated) NormalHit damage other bonuses

The crit bonus applies. (and presumably all damage bonuses apply).
IT DOES NOT trigger extra FREEZE roll check when using ice weapons !
Double dips the *3 multiplier of explosive vs frozen . (also fire vs health and corrosive vs armor)

# Normal Hit =  519.53961 using        Bratchny ; Scaled Base Gun Damage (CARD) =  388.53278 ; Sum of Additive Gun Damage Multiplier    0.33718 (beware exceptions!! & AMP SHIELD)  
# Damage Type =          COLD ; ElementalMul = 1.00000; ( GrenadeMul = 1.08739 ); address =    CF0E018 
# CRIT !!! ;(gun)Crit Multiplier = 4.595  
# vsHealthorArmorMul 1.00; Intermediary Damage Value 2387.16870  
       2562     5621.864 Max       847.526 Cur     3234.695 Prev     2387.169 Damage   4387AF18 baseaddress    Lil' Darksider vsHealthOrArmor 
# Chance to trigger effect 1.0000 * 15.0000 * 1.0000 * 1.2505 * 1.5000 * 0.9000 * 1.0000 * 1.0000 * 1.0000 * 1.0000 = 0.2532  
# vsHealthorArmorMul 1.00; Intermediary Damage Value 381.94699  
         16     5621.864 Max       465.579 Cur      847.526 Prev      381.947 Damage   4387AF18 baseaddress    Lil' Darksider vsHealthOrArmor 

// calculation had 2/5 integrity
2387.169 * 0.16 = 381.94704  

// double dip multiplier explosive vs frozen test
# Normal Hit =  704.12885 using        Injector ; Scaled Base Gun Damage (CARD) =  396.45065 ; Sum of Additive Gun Damage Multiplier    0.77608 (beware exceptions!! & AMP SHIELD)  
# Damage Type =     EXPLOSIVE ; ElementalMul = 1.00000; ( GrenadeMul = 1.43739 ); address =    CF0E018 
# vsHealthorArmorMul 3.00; Intermediary Damage Value 633.71594  
        172    65240.727 Max     16886.137 Cur    18787.285 Prev     1901.148 Damage   43872958 baseaddress       Fair Dinkum vsHealthOrArmor 
# Damage Type =     EXPLOSIVE ; ElementalMul = 1.00000; ( GrenadeMul = 1.43739 ); address =    CF0E018 
# vsHealthorArmorMul 3.00; Intermediary Damage Value 182.17921  
# Damage Type =     EXPLOSIVE ; ElementalMul = 1.00000; ( GrenadeMul = 1.43739 ); address =    CF0E018 
# vsHealthorArmorMul 3.00; Intermediary Damage Value 182.17921  
# Damage Type =     EXPLOSIVE ; ElementalMul = 1.00000; ( GrenadeMul = 1.43739 ); address =    CF0E018 
# vsHealthorArmorMul 3.00; Intermediary Damage Value 182.17921  
# Damage Type =     EXPLOSIVE ; ElementalMul = 1.00000; ( GrenadeMul = 1.43739 ); address =    CF0E018 
# vsHealthorArmorMul 3.00; Intermediary Damage Value 182.17921  
# Damage Type =     EXPLOSIVE ; ElementalMul = 1.00000; ( GrenadeMul = 1.43739 ); address =    CF0E018 
# vsHealthorArmorMul 3.00; Intermediary Damage Value 182.17921  
         46    65240.727 Max     14153.448 Cur    16886.137 Prev     2732.688 Damage   43872958 baseaddress       Fair Dinkum vsHealthOrArmor 
# Damage Type =     EXPLOSIVE ; ElementalMul = 1.00000; ( GrenadeMul = 1.43739 ); address =    CF0E018 
# vsHealthorArmorMul 3.00; Intermediary Damage Value 273.76529  
         47    65240.727 Max     13332.152 Cur    14153.448 Prev      821.296 Damage   43872958 baseaddress       Fair Dinkum vsHealthOrArmor 

//calculation verification
704.12885 * 0.9 * 3 = 1901.14789 // impact damage lvl scaling *0.9
704.12885 * 0.9 * 1.43739  /5 = 182.1793981 // the splash 
total splash damage = 182.1793981 *5 *3 = 2732.6909 
Integrity : 1901.14789 * 0.16 =  304.183  // error log said  273.76529   I'M PRETTY SURE THIS IS ME LEAKING OXYGEN FROM MY TRANQUILITY OZ KIT. 
And then this 273.76529 IS MULTIPLIED **AGAIN** by * explosive vs frozen =  821.296 integrity 2/5 damage